Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ cos^2a/(2sin^2a-1)+sin^2a/(2cos^2a-1)

¿Cómo vas a descomponer esta cos^2a/(2sin^2a-1)+sin^2a/(2cos^2a-1) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
      2               2      
   cos (a)         sin (a)   
------------- + -------------
     2               2       
2*sin (a) - 1   2*cos (a) - 1
sin⁡2(a)2cos⁡2(a)−1+cos⁡2(a)2sin⁡2(a)−1\frac{\sin^{2}{\left(a \right)}}{2 \cos^{2}{\left(a \right)} - 1} + \frac{\cos^{2}{\left(a \right)}}{2 \sin^{2}{\left(a \right)} - 1} 
cos(a)^2/(2*sin(a)^2 - 1) + sin(a)^2/(2*cos(a)^2 - 1)
Simplificación general [src] 
-1
−1-1 
-1
Denominador racional [src] 
   2    /          2   \      2    /          2   \
cos (a)*\-1 + 2*cos (a)/ + sin (a)*\-1 + 2*sin (a)/
---------------------------------------------------
         /          2   \ /          2   \         
         \-1 + 2*cos (a)/*\-1 + 2*sin (a)/
(2sin⁡2(a)−1)sin⁡2(a)+(2cos⁡2(a)−1)cos⁡2(a)(2sin⁡2(a)−1)(2cos⁡2(a)−1)\frac{\left(2 \sin^{2}{\left(a \right)} - 1\right) \sin^{2}{\left(a \right)} + \left(2 \cos^{2}{\left(a \right)} - 1\right) \cos^{2}{\left(a \right)}}{\left(2 \sin^{2}{\left(a \right)} - 1\right) \left(2 \cos^{2}{\left(a \right)} - 1\right)} 
(cos(a)^2*(-1 + 2*cos(a)^2) + sin(a)^2*(-1 + 2*sin(a)^2))/((-1 + 2*cos(a)^2)*(-1 + 2*sin(a)^2))
Potencias [src] 
                 2                                 
   / I*a    -I*a\                                  
   |e      e    |                            2     
   |---- + -----|            /   -I*a    I*a\      
   \ 2       2  /            \- e     + e   /      
---------------------- - --------------------------
                     2     /                     2\
     /   -I*a    I*a\      |       / I*a    -I*a\ |
     \- e     + e   /      |       |e      e    | |
-1 - -----------------   4*|-1 + 2*|---- + -----| |
             2             \       \ 2       2  / /
(eia2+e−ia2)2−(eia−e−ia)22−1−(eia−e−ia)24(2(eia2+e−ia2)2−1)\frac{\left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{2}}{- \frac{\left(e^{i a} - e^{- i a}\right)^{2}}{2} - 1} - \frac{\left(e^{i a} - e^{- i a}\right)^{2}}{4 \left(2 \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{2} - 1\right)} 
(exp(i*a)/2 + exp(-i*a)/2)^2/(-1 - (-exp(-i*a) + exp(i*a))^2/2) - (-exp(-i*a) + exp(i*a))^2/(4*(-1 + 2*(exp(i*a)/2 + exp(-i*a)/2)^2))
Denominador común [src] 
      2         2           4           4    
 - cos (a) - sin (a) + 2*cos (a) + 2*sin (a) 
---------------------------------------------
         2           2           2       2   
1 - 2*cos (a) - 2*sin (a) + 4*cos (a)*sin (a)
2sin⁡4(a)−sin⁡2(a)+2cos⁡4(a)−cos⁡2(a)4sin⁡2(a)cos⁡2(a)−2sin⁡2(a)−2cos⁡2(a)+1\frac{2 \sin^{4}{\left(a \right)} - \sin^{2}{\left(a \right)} + 2 \cos^{4}{\left(a \right)} - \cos^{2}{\left(a \right)}}{4 \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} - 2 \sin^{2}{\left(a \right)} - 2 \cos^{2}{\left(a \right)} + 1} 
(-cos(a)^2 - sin(a)^2 + 2*cos(a)^4 + 2*sin(a)^4)/(1 - 2*cos(a)^2 - 2*sin(a)^2 + 4*cos(a)^2*sin(a)^2)
Respuesta numérica [src] 
sin(a)^2/(-1.0 + 2.0*cos(a)^2) + cos(a)^2/(-1.0 + 2.0*sin(a)^2)
sin(a)^2/(-1.0 + 2.0*cos(a)^2) + cos(a)^2/(-1.0 + 2.0*sin(a)^2)
Combinatoria [src] 
     2         2           4           4   
- cos (a) - sin (a) + 2*cos (a) + 2*sin (a)
-------------------------------------------
     /          2   \ /          2   \     
     \-1 + 2*cos (a)/*\-1 + 2*sin (a)/
2sin⁡4(a)−sin⁡2(a)+2cos⁡4(a)−cos⁡2(a)(2sin⁡2(a)−1)(2cos⁡2(a)−1)\frac{2 \sin^{4}{\left(a \right)} - \sin^{2}{\left(a \right)} + 2 \cos^{4}{\left(a \right)} - \cos^{2}{\left(a \right)}}{\left(2 \sin^{2}{\left(a \right)} - 1\right) \left(2 \cos^{2}{\left(a \right)} - 1\right)} 
(-cos(a)^2 - sin(a)^2 + 2*cos(a)^4 + 2*sin(a)^4)/((-1 + 2*cos(a)^2)*(-1 + 2*sin(a)^2))
Unión de expresiones racionales [src] 
   2    /          2   \      2    /          2   \
cos (a)*\-1 + 2*cos (a)/ + sin (a)*\-1 + 2*sin (a)/
---------------------------------------------------
         /          2   \ /          2   \         
         \-1 + 2*cos (a)/*\-1 + 2*sin (a)/
(2sin⁡2(a)−1)sin⁡2(a)+(2cos⁡2(a)−1)cos⁡2(a)(2sin⁡2(a)−1)(2cos⁡2(a)−1)\frac{\left(2 \sin^{2}{\left(a \right)} - 1\right) \sin^{2}{\left(a \right)} + \left(2 \cos^{2}{\left(a \right)} - 1\right) \cos^{2}{\left(a \right)}}{\left(2 \sin^{2}{\left(a \right)} - 1\right) \left(2 \cos^{2}{\left(a \right)} - 1\right)} 
(cos(a)^2*(-1 + 2*cos(a)^2) + sin(a)^2*(-1 + 2*sin(a)^2))/((-1 + 2*cos(a)^2)*(-1 + 2*sin(a)^2))
Parte trigonométrica [src] 
                        2                                                     
          /        2/a\\                                   2/a\               
          |-1 + cot |-||                              4*cot |-|               
          \         \2//                                    \2/               
------------------------------------ + ---------------------------------------
               /            2/a\   \                  /                     2\
             2 |       8*cot |-|   |                  |       /        2/a\\ |
/       2/a\\  |             \2/   |                2 |     2*|-1 + cot |-|| |
|1 + cot |-|| *|-1 + --------------|   /       2/a\\  |       \         \2// |
\        \2//  |                  2|   |1 + cot |-|| *|-1 + -----------------|
               |     /       2/a\\ |   \        \2//  |                    2 |
               |     |1 + cot |-|| |                  |       /       2/a\\  |
               \     \        \2// /                  |       |1 + cot |-||  |
                                                      \       \        \2//  /
4cot⁡2(a2)(2(cot⁡2(a2)−1)2(cot⁡2(a2)+1)2−1)(cot⁡2(a2)+1)2+(cot⁡2(a2)−1)2(−1+8cot⁡2(a2)(cot⁡2(a2)+1)2)(cot⁡2(a2)+1)2\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(-1 + \frac{8 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} 
    2/    pi\                       
 sin |a + --|             2         
     \    2 /          sin (a)      
-------------- + -------------------
          2                2/    pi\
-1 + 2*sin (a)   -1 + 2*sin |a + --|
                            \    2 /
sin⁡2(a)2sin⁡2(a+π2)−1+sin⁡2(a+π2)2sin⁡2(a)−1\frac{\sin^{2}{\left(a \right)}}{2 \sin^{2}{\left(a + \frac{\pi}{2} \right)} - 1} + \frac{\sin^{2}{\left(a + \frac{\pi}{2} \right)}}{2 \sin^{2}{\left(a \right)} - 1} 
          1                        1           
---------------------- + ----------------------
/        2   \    2      /        2   \    2   
|-1 + -------|*sec (a)   |-1 + -------|*csc (a)
|        2   |           |        2   |        
\     csc (a)/           \     sec (a)/
1(−1+2sec⁡2(a))csc⁡2(a)+1(−1+2csc⁡2(a))sec⁡2(a)\frac{1}{\left(-1 + \frac{2}{\sec^{2}{\left(a \right)}}\right) \csc^{2}{\left(a \right)}} + \frac{1}{\left(-1 + \frac{2}{\csc^{2}{\left(a \right)}}\right) \sec^{2}{\left(a \right)}} 
             1                             1             
--------------------------- + ---------------------------
/        2   \    2/    pi\   /          2      \    2   
|-1 + -------|*sec |a - --|   |-1 + ------------|*sec (a)
|        2   |     \    2 /   |        2/    pi\|        
\     sec (a)/                |     sec |a - --||        
                              \         \    2 //
1(−1+2sec⁡2(a−π2))sec⁡2(a)+1(−1+2sec⁡2(a))sec⁡2(a−π2)\frac{1}{\left(-1 + \frac{2}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}\right) \sec^{2}{\left(a \right)}} + \frac{1}{\left(-1 + \frac{2}{\sec^{2}{\left(a \right)}}\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}} 
             1                             1             
--------------------------- + ---------------------------
/        2   \    2/pi    \   /          2      \    2   
|-1 + -------|*csc |-- - a|   |-1 + ------------|*csc (a)
|        2   |     \2     /   |        2/pi    \|        
\     csc (a)/                |     csc |-- - a||        
                              \         \2     //
1(−1+2csc⁡2(−a+π2))csc⁡2(a)+1(−1+2csc⁡2(a))csc⁡2(−a+π2)\frac{1}{\left(-1 + \frac{2}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(a \right)}} + \frac{1}{\left(-1 + \frac{2}{\csc^{2}{\left(a \right)}}\right) \csc^{2}{\left(- a + \frac{\pi}{2} \right)}} 
                        2                                                    
           /       2/a\\                                  2/a\               
           |1 - tan |-||                             4*tan |-|               
           \        \2//                                   \2/               
------------------------------------ + --------------------------------------
               /            2/a\   \                  /                    2\
             2 |       8*tan |-|   |                  |       /       2/a\\ |
/       2/a\\  |             \2/   |                2 |     2*|1 - tan |-|| |
|1 + tan |-|| *|-1 + --------------|   /       2/a\\  |       \        \2// |
\        \2//  |                  2|   |1 + tan |-|| *|-1 + ----------------|
               |     /       2/a\\ |   \        \2//  |                   2 |
               |     |1 + tan |-|| |                  |      /       2/a\\  |
               \     \        \2// /                  |      |1 + tan |-||  |
                                                      \      \        \2//  /
4tan⁡2(a2)(2(1−tan⁡2(a2))2(tan⁡2(a2)+1)2−1)(tan⁡2(a2)+1)2+(1−tan⁡2(a2))2(−1+8tan⁡2(a2)(tan⁡2(a2)+1)2)(tan⁡2(a2)+1)2\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - 1\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{2}}{\left(-1 + \frac{8 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} 
    2/    pi\                       
 cos |a - --|             2         
     \    2 /          cos (a)      
-------------- + -------------------
          2                2/    pi\
-1 + 2*cos (a)   -1 + 2*cos |a - --|
                            \    2 /
cos⁡2(a)2cos⁡2(a−π2)−1+cos⁡2(a−π2)2cos⁡2(a)−1\frac{\cos^{2}{\left(a \right)}}{2 \cos^{2}{\left(a - \frac{\pi}{2} \right)} - 1} + \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{2 \cos^{2}{\left(a \right)} - 1} 
-1
−1-1 
-1
    © Sr Examen – Калькулятор