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Simplificación de expresiones/ Descomposición en fracciones simples/ sin^2t-(cos(пи/2+t)sin(пи-t))/(tg(пи-t)ctg(3пи/2+t))

¿Cómo vas a descomponer esta sin^2t-(cos(пи/2+t)sin(пи-t))/(tg(пи-t)ctg(3пи/2+t)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
              /pi    \             
           cos|-- + t|*sin(pi - t) 
   2          \2     /             
sin (t) - -------------------------
                         /3*pi    \
          tan(pi - t)*cot|---- + t|
                         \ 2      /
−sin⁡(π−t)cos⁡(t+π2)tan⁡(π−t)cot⁡(t+3π2)+sin⁡2(t)- \frac{\sin{\left(\pi - t \right)} \cos{\left(t + \frac{\pi}{2} \right)}}{\tan{\left(\pi - t \right)} \cot{\left(t + \frac{3 \pi}{2} \right)}} + \sin^{2}{\left(t \right)} 
sin(t)^2 - cos(pi/2 + t)*sin(pi - t)/(tan(pi - t)*cot((3*pi)/2 + t))
Simplificación general [src] 
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Respuesta numérica [src] 
sin(t)^2 - cos(pi/2 + t)*sin(pi - t)/(cot((3*pi)/2 + t)*tan(pi - t))
sin(t)^2 - cos(pi/2 + t)*sin(pi - t)/(cot((3*pi)/2 + t)*tan(pi - t))
Unión de expresiones racionales [src] 
/   /2*t + 3*pi\                    /pi + 2*t\\       
|cot|----------|*sin(t)*tan(t) + cos|--------||*sin(t)
\   \    2     /                    \   2    //       
------------------------------------------------------
                   /2*t + 3*pi\                       
                cot|----------|*tan(t)                
                   \    2     /
(sin⁡(t)tan⁡(t)cot⁡(2t+3π2)+cos⁡(2t+π2))sin⁡(t)tan⁡(t)cot⁡(2t+3π2)\frac{\left(\sin{\left(t \right)} \tan{\left(t \right)} \cot{\left(\frac{2 t + 3 \pi}{2} \right)} + \cos{\left(\frac{2 t + \pi}{2} \right)}\right) \sin{\left(t \right)}}{\tan{\left(t \right)} \cot{\left(\frac{2 t + 3 \pi}{2} \right)}} 
(cot((2*t + 3*pi)/2)*sin(t)*tan(t) + cos((pi + 2*t)/2))*sin(t)/(cot((2*t + 3*pi)/2)*tan(t))
Combinatoria [src] 
   2    /       2   \
sin (t)*\1 + tan (t)/
---------------------
          2          
       tan (t)
(tan⁡2(t)+1)sin⁡2(t)tan⁡2(t)\frac{\left(\tan^{2}{\left(t \right)} + 1\right) \sin^{2}{\left(t \right)}}{\tan^{2}{\left(t \right)}} 
sin(t)^2*(1 + tan(t)^2)/tan(t)^2
Potencias [src] 
             2   
   2      sin (t)
sin (t) + -------
             2   
          tan (t)
sin⁡2(t)+sin⁡2(t)tan⁡2(t)\sin^{2}{\left(t \right)} + \frac{\sin^{2}{\left(t \right)}}{\tan^{2}{\left(t \right)}} 
                      /   /    pi\      /     pi\\                                                          
                      | I*|t + --|    I*|-t - --||                                                          
                      |   \    2 /      \     2 /|                                                          
                  2   |e             e           | /   I*(t - pi)    I*(pi - t)\ / I*(pi - t)    I*(t - pi)\
  /   -I*t    I*t\    |----------- + ------------|*\- e           + e          /*\e           + e          /
  \- e     + e   /    \     2             2      /                                                          
- ----------------- - --------------------------------------------------------------------------------------
          4                                     /   I*(pi - t)    I*(t - pi)\                               
                                              2*\- e           + e          /*tan(t)
−(eit−e−it)24−(ei(π−t)−ei(t−π))(ei(π−t)+ei(t−π))(ei(−t−π2)2+ei(t+π2)2)2(−ei(π−t)+ei(t−π))tan⁡(t)- \frac{\left(e^{i t} - e^{- i t}\right)^{2}}{4} - \frac{\left(e^{i \left(\pi - t\right)} - e^{i \left(t - \pi\right)}\right) \left(e^{i \left(\pi - t\right)} + e^{i \left(t - \pi\right)}\right) \left(\frac{e^{i \left(- t - \frac{\pi}{2}\right)}}{2} + \frac{e^{i \left(t + \frac{\pi}{2}\right)}}{2}\right)}{2 \left(- e^{i \left(\pi - t\right)} + e^{i \left(t - \pi\right)}\right) \tan{\left(t \right)}} 
-(-exp(-i*t) + exp(i*t))^2/4 - (exp(i*(t + pi/2))/2 + exp(i*(-t - pi/2))/2)*(-exp(i*(t - pi)) + exp(i*(pi - t)))*(exp(i*(pi - t)) + exp(i*(t - pi)))/(2*(-exp(i*(pi - t)) + exp(i*(t - pi)))*tan(t))
Denominador común [src] 
   2      sin(t)*sin(pi - t)
sin (t) - ------------------
          tan(t)*tan(pi - t)
sin⁡2(t)−sin⁡(t)sin⁡(π−t)tan⁡(t)tan⁡(π−t)\sin^{2}{\left(t \right)} - \frac{\sin{\left(t \right)} \sin{\left(\pi - t \right)}}{\tan{\left(t \right)} \tan{\left(\pi - t \right)}} 
sin(t)^2 - sin(t)*sin(pi - t)/(tan(t)*tan(pi - t))
Abrimos la expresión [src] 
             2   
   2      sin (t)
sin (t) + -------
             2   
          tan (t)
sin⁡2(t)+sin⁡2(t)tan⁡2(t)\sin^{2}{\left(t \right)} + \frac{\sin^{2}{\left(t \right)}}{\tan^{2}{\left(t \right)}} 
              /pi    \             
           cos|-- + t|*sin(pi - t) 
   2          \2     /             
sin (t) - -------------------------
             /3*pi    \            
          cot|---- + t|*tan(pi - t)
             \ 2      /
sin⁡2(t)−sin⁡(π−t)cos⁡(t+π2)tan⁡(π−t)cot⁡(t+3π2)\sin^{2}{\left(t \right)} - \frac{\sin{\left(\pi - t \right)} \cos{\left(t + \frac{\pi}{2} \right)}}{\tan{\left(\pi - t \right)} \cot{\left(t + \frac{3 \pi}{2} \right)}} 
sin(t)^2 - cos(pi/2 + t)*sin(pi - t)/(cot((3*pi)/2 + t)*tan(pi - t))
Parte trigonométrica [src] 
   1             csc(t)      
------- + -------------------
   2         2       /pi    \
csc (t)   sec (t)*sec|-- - t|
                     \2     /
csc⁡(t)sec⁡2(t)sec⁡(−t+π2)+1csc⁡2(t)\frac{\csc{\left(t \right)}}{\sec^{2}{\left(t \right)} \sec{\left(- t + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(t \right)}} 
                         2/    pi\       
                      sec |t - --|       
     1                    \    2 /       
------------ + --------------------------
   2/    pi\             2       /pi    \
sec |t - --|   csc(t)*sec (t)*sec|-- - t|
    \    2 /                     \2     /
1sec⁡2(t−π2)+sec⁡2(t−π2)csc⁡(t)sec⁡2(t)sec⁡(−t+π2)\frac{1}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}} + \frac{\sec^{2}{\left(t - \frac{\pi}{2} \right)}}{\csc{\left(t \right)} \sec^{2}{\left(t \right)} \sec{\left(- t + \frac{\pi}{2} \right)}} 
                                                /        2/t   pi\\
                                                |     sec |- - --||
                    2/    pi\ /         1     \ |         \2   4 /|
                 sec |t - --|*|1 + -----------|*|-1 + ------------|
                     \    2 / |       /    pi\| |        2/t   pi\|
                              |    sec|t - --|| |     sec |- + --||
1       1                     \       \    2 // \         \2   4 //
- - ---------- - --------------------------------------------------
2   2*sec(2*t)                  2       /t\    /t   pi\            
                             sec (t)*sec|-|*sec|- - --|            
                                        \2/    \2   2 /
−(1+1sec⁡(t−π2))(sec⁡2(t2−π4)sec⁡2(t2+π4)−1)sec⁡2(t−π2)sec⁡(t2)sec⁡2(t)sec⁡(t2−π2)+12−12sec⁡(2t)- \frac{\left(1 + \frac{1}{\sec{\left(t - \frac{\pi}{2} \right)}}\right) \left(\frac{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}} - 1\right) \sec^{2}{\left(t - \frac{\pi}{2} \right)}}{\sec{\left(\frac{t}{2} \right)} \sec^{2}{\left(t \right)} \sec{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + \frac{1}{2} - \frac{1}{2 \sec{\left(2 t \right)}} 
                      2/    pi\ /       1   \
                 2*sec |t - --|*|-1 + ------|
1       1              \    2 / \     sec(t)/
- - ---------- - ----------------------------
2   2*sec(2*t)    /         2/t\   \         
                  |      sec |-|   |         
                  |          \2/   |    2    
                  |1 + ------------|*sec (t) 
                  |       2/t   pi\|         
                  |    sec |- - --||         
                  \        \2   2 //
−2(−1+1sec⁡(t))sec⁡2(t−π2)(sec⁡2(t2)sec⁡2(t2−π2)+1)sec⁡2(t)+12−12sec⁡(2t)- \frac{2 \left(-1 + \frac{1}{\sec{\left(t \right)}}\right) \sec^{2}{\left(t - \frac{\pi}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{t}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec^{2}{\left(t \right)}} + \frac{1}{2} - \frac{1}{2 \sec{\left(2 t \right)}} 
       2/t\           /       2/t   pi\\           /t\  
  4*tan |-|         2*|1 - tan |- + --||*cot(t)*cot|-|  
        \2/           \        \2   4 //           \2/  
-------------- - ---------------------------------------
             2   /       2/t\\ /       2/t   pi\\       
/       2/t\\    |1 + cot |-||*|1 + tan |- + --||*tan(t)
|1 + tan |-||    \        \2// \        \2   4 //       
\        \2//
−2(1−tan⁡2(t2+π4))cot⁡(t2)cot⁡(t)(tan⁡2(t2+π4)+1)(cot⁡2(t2)+1)tan⁡(t)+4tan⁡2(t2)(tan⁡2(t2)+1)2- \frac{2 \left(1 - \tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}\right) \cot{\left(\frac{t}{2} \right)} \cot{\left(t \right)}}{\left(\tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right) \tan{\left(t \right)}} + \frac{4 \tan^{2}{\left(\frac{t}{2} \right)}}{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}} 
                                         /        2/t   pi\\                   
                                         |     cos |- + --||                   
                  2    /       /    pi\\ |         \2   4 /|    /t\    /t   pi\
               cos (t)*|1 + cos|t - --||*|-1 + ------------|*cos|-|*cos|- - --|
                       \       \    2 // |        2/t   pi\|    \2/    \2   2 /
                                         |     cos |- - --||                   
1   cos(2*t)                             \         \2   4 //                   
- - -------- - ----------------------------------------------------------------
2      2                                    2/    pi\                          
                                         cos |t - --|                          
                                             \    2 /
−(−1+cos⁡2(t2+π4)cos⁡2(t2−π4))(cos⁡(t−π2)+1)cos⁡(t2)cos⁡2(t)cos⁡(t2−π2)cos⁡2(t−π2)−cos⁡(2t)2+12- \frac{\left(-1 + \frac{\cos^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{4} \right)}}\right) \left(\cos{\left(t - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{t}{2} \right)} \cos^{2}{\left(t \right)} \cos{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(t - \frac{\pi}{2} \right)}} - \frac{\cos{\left(2 t \right)}}{2} + \frac{1}{2} 
                                     /           /t\ \                           
                                   2 |      2*tan|-| |                           
                      /       2/t\\  |           \2/ | /          1      \    /t\
                      |1 - tan |-|| *|1 + -----------|*|-1 + ------------|*tan|-|
                      \        \4//  |           2/t\| |        2/t   pi\|    \2/
             2                       |    1 + tan |-|| |     tan |- + --||       
1     1 - tan (t)                    \            \2// \         \2   4 //       
- - --------------- - -----------------------------------------------------------
2     /       2   \                                   2                          
    2*\1 + tan (t)/                      /       2/t\\     2                     
                                         |1 + tan |-|| *tan (t)                  
                                         \        \4//
−(−1+1tan⁡2(t2+π4))(1+2tan⁡(t2)tan⁡2(t2)+1)(1−tan⁡2(t4))2tan⁡(t2)(tan⁡2(t4)+1)2tan⁡2(t)−1−tan⁡2(t)2(tan⁡2(t)+1)+12- \frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{2 \tan{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1}\right) \left(1 - \tan^{2}{\left(\frac{t}{4} \right)}\right)^{2} \tan{\left(\frac{t}{2} \right)}}{\left(\tan^{2}{\left(\frac{t}{4} \right)} + 1\right)^{2} \tan^{2}{\left(t \right)}} - \frac{1 - \tan^{2}{\left(t \right)}}{2 \left(\tan^{2}{\left(t \right)} + 1\right)} + \frac{1}{2} 
1 - cos(2*t)      2/t\    2                 /        2/t   pi\\    /t\
------------ - cos |-|*cot (t)*(1 + sin(t))*|-1 + cot |- + --||*tan|-|
     2             \2/                      \         \2   4 //    \2/
1−cos⁡(2t)2−(sin⁡(t)+1)(cot⁡2(t2+π4)−1)cos⁡2(t2)tan⁡(t2)cot⁡2(t)\frac{1 - \cos{\left(2 t \right)}}{2} - \left(\sin{\left(t \right)} + 1\right) \left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} - 1\right) \cos^{2}{\left(\frac{t}{2} \right)} \tan{\left(\frac{t}{2} \right)} \cot^{2}{\left(t \right)} 
                    2                 
1   cos(2*t)   2*cos (t)*(-1 + cos(t))
- - -------- - -----------------------
2      2            2           4/t\  
                 sin (t) + 4*sin |-|  
                                 \2/
−cos⁡(2t)2+12−2(cos⁡(t)−1)cos⁡2(t)4sin⁡4(t2)+sin⁡2(t)- \frac{\cos{\left(2 t \right)}}{2} + \frac{1}{2} - \frac{2 \left(\cos{\left(t \right)} - 1\right) \cos^{2}{\left(t \right)}}{4 \sin^{4}{\left(\frac{t}{2} \right)} + \sin^{2}{\left(t \right)}} 
   2         2   
cos (t) + sin (t)
sin⁡2(t)+cos⁡2(t)\sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)} 
   1           1      
------- + ------------
   2         2/pi    \
csc (t)   csc |-- - t|
              \2     /
1csc⁡2(−t+π2)+1csc⁡2(t)\frac{1}{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(t \right)}} 
                  2/t\              /        2/t   pi\\           /t\
               cos |-|*(1 + sin(t))*|-1 + cot |- + --||*cot(t)*tan|-|
1 - cos(2*t)       \2/              \         \2   4 //           \2/
------------ - ------------------------------------------------------
     2                                 tan(t)
1−cos⁡(2t)2−(sin⁡(t)+1)(cot⁡2(t2+π4)−1)cos⁡2(t2)tan⁡(t2)cot⁡(t)tan⁡(t)\frac{1 - \cos{\left(2 t \right)}}{2} - \frac{\left(\sin{\left(t \right)} + 1\right) \left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} - 1\right) \cos^{2}{\left(\frac{t}{2} \right)} \tan{\left(\frac{t}{2} \right)} \cot{\left(t \right)}}{\tan{\left(t \right)}} 
                                                                /           2       \
                       2/t\    2         2/pi   t\              |        cos (t)    |
                    sin |-|*sin (2*t)*sin |-- + -|*(1 + sin(t))*|-1 + --------------|
       /pi      \       \2/               \2    2/              |          4/t   pi\|
    sin|-- + 2*t|                                               |     4*sin |- + --||
1      \2       /                                               \           \2   4 //
- - ------------- - -----------------------------------------------------------------
2         2                                          5                               
                                                2*sin (t)
−(−1+cos⁡2(t)4sin⁡4(t2+π4))(sin⁡(t)+1)sin⁡2(t2)sin⁡2(2t)sin⁡2(t2+π2)2sin⁡5(t)−sin⁡(2t+π2)2+12- \frac{\left(-1 + \frac{\cos^{2}{\left(t \right)}}{4 \sin^{4}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}}\right) \left(\sin{\left(t \right)} + 1\right) \sin^{2}{\left(\frac{t}{2} \right)} \sin^{2}{\left(2 t \right)} \sin^{2}{\left(\frac{t}{2} + \frac{\pi}{2} \right)}}{2 \sin^{5}{\left(t \right)}} - \frac{\sin{\left(2 t + \frac{\pi}{2} \right)}}{2} + \frac{1}{2} 
                             2    /          1     \ 
                        2*csc (t)*|-1 + -----------| 
                                  |        /pi    \| 
                                  |     csc|-- - t|| 
1          1                      \        \2     // 
- - --------------- - -------------------------------
2        /pi      \   /       2/pi   t\\             
    2*csc|-- - 2*t|   |    csc |-- - -||             
         \2       /   |        \2    2/|    2/pi    \
                      |1 + ------------|*csc |-- - t|
                      |         2/t\   |     \2     /
                      |      csc |-|   |             
                      \          \2/   /
−2(−1+1csc⁡(−t+π2))csc⁡2(t)(1+csc⁡2(−t2+π2)csc⁡2(t2))csc⁡2(−t+π2)+12−12csc⁡(−2t+π2)- \frac{2 \left(-1 + \frac{1}{\csc{\left(- t + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(t \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{t}{2} \right)}}\right) \csc^{2}{\left(- t + \frac{\pi}{2} \right)}} + \frac{1}{2} - \frac{1}{2 \csc{\left(- 2 t + \frac{\pi}{2} \right)}} 
                         /            2/t\\
                         |     1 - tan |-||
                         |             \2/|
                       2*|-1 + -----------|
                         |            2/t\|
             2           |     1 + tan |-||
1     1 - tan (t)        \             \2//
- - --------------- - ---------------------
2     /       2   \   /       2/t\\    2   
    2*\1 + tan (t)/   |1 + tan |-||*tan (t)
                      \        \2//
−1−tan⁡2(t)2(tan⁡2(t)+1)−2(1−tan⁡2(t2)tan⁡2(t2)+1−1)(tan⁡2(t2)+1)tan⁡2(t)+12- \frac{1 - \tan^{2}{\left(t \right)}}{2 \left(\tan^{2}{\left(t \right)} + 1\right)} - \frac{2 \left(\frac{1 - \tan^{2}{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(\frac{t}{2} \right)} + 1} - 1\right)}{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right) \tan^{2}{\left(t \right)}} + \frac{1}{2} 
1
11 
                            2                                                
               /       2/t\\     4/t\              /          1      \    /t\
               |1 - tan |-|| *cos |-|*(1 + sin(t))*|-1 + ------------|*tan|-|
               \        \4//      \4/              |        2/t   pi\|    \2/
                                                   |     tan |- + --||       
1   cos(2*t)                                       \         \2   4 //       
- - -------- - --------------------------------------------------------------
2      2                                     2                               
                                          tan (t)
−(−1+1tan⁡2(t2+π4))(1−tan⁡2(t4))2(sin⁡(t)+1)cos⁡4(t4)tan⁡(t2)tan⁡2(t)−cos⁡(2t)2+12- \frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}}\right) \left(1 - \tan^{2}{\left(\frac{t}{4} \right)}\right)^{2} \left(\sin{\left(t \right)} + 1\right) \cos^{4}{\left(\frac{t}{4} \right)} \tan{\left(\frac{t}{2} \right)}}{\tan^{2}{\left(t \right)}} - \frac{\cos{\left(2 t \right)}}{2} + \frac{1}{2} 
1 - cos(2*t)      2*(-1 + cos(t))   
------------ - ---------------------
     2         /       2/t\\    2   
               |1 + tan |-||*tan (t)
               \        \2//
1−cos⁡(2t)2−2(cos⁡(t)−1)(tan⁡2(t2)+1)tan⁡2(t)\frac{1 - \cos{\left(2 t \right)}}{2} - \frac{2 \left(\cos{\left(t \right)} - 1\right)}{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right) \tan^{2}{\left(t \right)}} 
       /pi      \      2      /        /    pi\\
    sin|-- + 2*t|   sin (2*t)*|-1 + sin|t + --||
1      \2       /             \        \    2 //
- - ------------- - ----------------------------
2         2            /         4/t\\          
                       |    4*sin |-||          
                       |          \2/|    4     
                     2*|1 + ---------|*sin (t)  
                       |        2    |          
                       \     sin (t) /
−sin⁡(2t+π2)2+12−(sin⁡(t+π2)−1)sin⁡2(2t)2(4sin⁡4(t2)sin⁡2(t)+1)sin⁡4(t)- \frac{\sin{\left(2 t + \frac{\pi}{2} \right)}}{2} + \frac{1}{2} - \frac{\left(\sin{\left(t + \frac{\pi}{2} \right)} - 1\right) \sin^{2}{\left(2 t \right)}}{2 \left(\frac{4 \sin^{4}{\left(\frac{t}{2} \right)}}{\sin^{2}{\left(t \right)}} + 1\right) \sin^{4}{\left(t \right)}} 
   1         1   
------- + -------
   2         2   
csc (t)   sec (t)
1sec⁡2(t)+1csc⁡2(t)\frac{1}{\sec^{2}{\left(t \right)}} + \frac{1}{\csc^{2}{\left(t \right)}} 
       2/t\          /        2/t   pi\\           /t\  
  4*cot |-|        2*|-1 + cot |- + --||*cot(t)*tan|-|  
        \2/          \         \2   4 //           \2/  
-------------- - ---------------------------------------
             2   /       2/t   pi\\ /       2/t\\       
/       2/t\\    |1 + cot |- + --||*|1 + tan |-||*tan(t)
|1 + cot |-||    \        \2   4 // \        \2//       
\        \2//
4cot⁡2(t2)(cot⁡2(t2)+1)2−2(cot⁡2(t2+π4)−1)tan⁡(t2)cot⁡(t)(tan⁡2(t2)+1)(cot⁡2(t2+π4)+1)tan⁡(t)\frac{4 \cot^{2}{\left(\frac{t}{2} \right)}}{\left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}} - \frac{2 \left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} - 1\right) \tan{\left(\frac{t}{2} \right)} \cot{\left(t \right)}}{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(t \right)}} 
       2/t\                2    /        2/t   pi\\     
  4*cot |-|           2*cot (t)*|-1 + cot |- + --||     
        \2/                     \         \2   4 //     
-------------- - ---------------------------------------
             2   /       1   \ /       2/t   pi\\    /t\
/       2/t\\    |1 + -------|*|1 + cot |- + --||*cot|-|
|1 + cot |-||    |       2/t\| \        \2   4 //    \2/
\        \2//    |    cot |-||                          
                 \        \2//
4cot⁡2(t2)(cot⁡2(t2)+1)2−2(cot⁡2(t2+π4)−1)cot⁡2(t)(1+1cot⁡2(t2))(cot⁡2(t2+π4)+1)cot⁡(t2)\frac{4 \cot^{2}{\left(\frac{t}{2} \right)}}{\left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}} - \frac{2 \left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} - 1\right) \cot^{2}{\left(t \right)}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{t}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} + 1\right) \cot{\left(\frac{t}{2} \right)}} 
   2         2/    pi\
sin (t) + sin |t + --|
              \    2 /
sin⁡2(t)+sin⁡2(t+π2)\sin^{2}{\left(t \right)} + \sin^{2}{\left(t + \frac{\pi}{2} \right)} 
                        2                     
1   cos(2*t)       2*cos (t)*(-1 + cos(t))    
- - -------- - -------------------------------
2      2       /       2/t   pi\\             
               |    cos |- - --||             
               |        \2   2 /|    2/    pi\
               |1 + ------------|*cos |t - --|
               |         2/t\   |     \    2 /
               |      cos |-|   |             
               \          \2/   /
−cos⁡(2t)2+12−2(cos⁡(t)−1)cos⁡2(t)(1+cos⁡2(t2−π2)cos⁡2(t2))cos⁡2(t−π2)- \frac{\cos{\left(2 t \right)}}{2} + \frac{1}{2} - \frac{2 \left(\cos{\left(t \right)} - 1\right) \cos^{2}{\left(t \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} \right)}}\right) \cos^{2}{\left(t - \frac{\pi}{2} \right)}} 
   2/    pi\                     
cos |t - --| - cos(t)*cos(pi + t)
    \    2 /
−cos⁡(t)cos⁡(t+π)+cos⁡2(t−π2)- \cos{\left(t \right)} \cos{\left(t + \pi \right)} + \cos^{2}{\left(t - \frac{\pi}{2} \right)} 
                                              /           /t\ \                    
                                    2         |      2*cot|-| |                    
                      /        2/t\\     2    |           \2/ | /        2/t   pi\\
                      |-1 + cot |-|| *cot (t)*|1 + -----------|*|-1 + cot |- + --||
                      \         \4//          |           2/t\| \         \2   4 //
              2                               |    1 + cot |-||                    
1     -1 + cot (t)                            \            \2//                    
- - --------------- - -------------------------------------------------------------
2     /       2   \                                    2                           
    2*\1 + cot (t)/                       /       2/t\\     /t\                    
                                          |1 + cot |-|| *cot|-|                    
                                          \        \4//     \2/
−(1+2cot⁡(t2)cot⁡2(t2)+1)(cot⁡2(t4)−1)2(cot⁡2(t2+π4)−1)cot⁡2(t)(cot⁡2(t4)+1)2cot⁡(t2)−cot⁡2(t)−12(cot⁡2(t)+1)+12- \frac{\left(1 + \frac{2 \cot{\left(\frac{t}{2} \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{t}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} - 1\right) \cot^{2}{\left(t \right)}}{\left(\cot^{2}{\left(\frac{t}{4} \right)} + 1\right)^{2} \cot{\left(\frac{t}{2} \right)}} - \frac{\cot^{2}{\left(t \right)} - 1}{2 \left(\cot^{2}{\left(t \right)} + 1\right)} + \frac{1}{2} 
                             2                                                        
1   cos(2*t)   /        2/t\\     2       4/t\              /        2/t   pi\\    /t\
- - -------- - |-1 + cot |-|| *cot (t)*sin |-|*(1 + sin(t))*|-1 + cot |- + --||*tan|-|
2      2       \         \4//              \4/              \         \2   4 //    \2/
−(sin⁡(t)+1)(cot⁡2(t4)−1)2(cot⁡2(t2+π4)−1)sin⁡4(t4)tan⁡(t2)cot⁡2(t)−cos⁡(2t)2+12- \left(\sin{\left(t \right)} + 1\right) \left(\cot^{2}{\left(\frac{t}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} - 1\right) \sin^{4}{\left(\frac{t}{4} \right)} \tan{\left(\frac{t}{2} \right)} \cot^{2}{\left(t \right)} - \frac{\cos{\left(2 t \right)}}{2} + \frac{1}{2} 
       2/t\                      /       2/t   pi\\             
  4*tan |-|                    2*|1 - tan |- + --||             
        \2/                      \        \2   4 //             
-------------- - -----------------------------------------------
             2   /       1   \ /       2/t   pi\\    2       /t\
/       2/t\\    |1 + -------|*|1 + tan |- + --||*tan (t)*tan|-|
|1 + tan |-||    |       2/t\| \        \2   4 //            \2/
\        \2//    |    tan |-||                                  
                 \        \2//
4tan⁡2(t2)(tan⁡2(t2)+1)2−2(1−tan⁡2(t2+π4))(1+1tan⁡2(t2))(tan⁡2(t2+π4)+1)tan⁡(t2)tan⁡2(t)\frac{4 \tan^{2}{\left(\frac{t}{2} \right)}}{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}} - \frac{2 \left(1 - \tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}\right)}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{t}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(\frac{t}{2} \right)} \tan^{2}{\left(t \right)}} 
                                /             2/t\\
                                |     -1 + cot |-||
                           2    |              \2/|
                      2*cot (t)*|-1 + ------------|
                                |            2/t\ |
              2                 |     1 + cot |-| |
1     -1 + cot (t)              \             \2/ /
- - --------------- - -----------------------------
2     /       2   \                   1            
    2*\1 + cot (t)/            1 + -------         
                                      2/t\         
                                   cot |-|         
                                       \2/
−cot⁡2(t)−12(cot⁡2(t)+1)+12−2(cot⁡2(t2)−1cot⁡2(t2)+1−1)cot⁡2(t)1+1cot⁡2(t2)- \frac{\cot^{2}{\left(t \right)} - 1}{2 \left(\cot^{2}{\left(t \right)} + 1\right)} + \frac{1}{2} - \frac{2 \left(\frac{\cot^{2}{\left(\frac{t}{2} \right)} - 1}{\cot^{2}{\left(\frac{t}{2} \right)} + 1} - 1\right) \cot^{2}{\left(t \right)}}{1 + \frac{1}{\cot^{2}{\left(\frac{t}{2} \right)}}} 
                                           /         2/t   pi\ \
                                           |      csc |- + --| |
                         2    /      1   \ |          \2   4 / |
                      csc (t)*|1 + ------|*|-1 + --------------|
                              \    csc(t)/ |        2/  t   pi\|
                                           |     csc |- - + --||
1          1                               \         \  2   4 //
- - --------------- - ------------------------------------------
2        /pi      \           /t\    2/pi    \    /pi   t\      
    2*csc|-- - 2*t|        csc|-|*csc |-- - t|*csc|-- - -|      
         \2       /           \2/     \2     /    \2    2/
−(−1+csc⁡2(t2+π4)csc⁡2(−t2+π4))(1+1csc⁡(t))csc⁡2(t)csc⁡(t2)csc⁡2(−t+π2)csc⁡(−t2+π2)+12−12csc⁡(−2t+π2)- \frac{\left(-1 + \frac{\csc^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{1}{\csc{\left(t \right)}}\right) \csc^{2}{\left(t \right)}}{\csc{\left(\frac{t}{2} \right)} \csc^{2}{\left(- t + \frac{\pi}{2} \right)} \csc{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}} + \frac{1}{2} - \frac{1}{2 \csc{\left(- 2 t + \frac{\pi}{2} \right)}} 
             2               
   2      cos (t)*sin(pi + t)
sin (t) - -------------------
                 sin(t)
sin⁡2(t)−sin⁡(t+π)cos⁡2(t)sin⁡(t)\sin^{2}{\left(t \right)} - \frac{\sin{\left(t + \pi \right)} \cos^{2}{\left(t \right)}}{\sin{\left(t \right)}} 
sin(t)^2 - cos(t)^2*sin(pi + t)/sin(t)
Compilar la expresión [src] 
              /pi    \             
           cos|-- + t|*sin(pi - t) 
   2          \2     /             
sin (t) - -------------------------
             /3*pi    \            
          cot|---- + t|*tan(pi - t)
             \ 2      /
sin⁡2(t)−sin⁡(π−t)cos⁡(t+π2)tan⁡(π−t)cot⁡(t+3π2)\sin^{2}{\left(t \right)} - \frac{\sin{\left(\pi - t \right)} \cos{\left(t + \frac{\pi}{2} \right)}}{\tan{\left(\pi - t \right)} \cot{\left(t + \frac{3 \pi}{2} \right)}} 
sin(t)^2 - cos(pi/2 + t)*sin(pi - t)/(cot((3*pi)/2 + t)*tan(pi - t))
Denominador racional [src] 
   2       2         /    pi\       
sin (t)*tan (t) - cos|t + --|*sin(t)
                     \    2 /       
------------------------------------
                 2                  
              tan (t)
sin⁡2(t)tan⁡2(t)−sin⁡(t)cos⁡(t+π2)tan⁡2(t)\frac{\sin^{2}{\left(t \right)} \tan^{2}{\left(t \right)} - \sin{\left(t \right)} \cos{\left(t + \frac{\pi}{2} \right)}}{\tan^{2}{\left(t \right)}} 
(sin(t)^2*tan(t)^2 - cos(t + pi/2)*sin(t))/tan(t)^2
    © Sr Examen – Калькулятор