Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
¿cómo vas a descomponer esta expresión en fracciones?:
((z-2)/(4*(z+2)^2))/(z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z))
x^3*y^12/(x*y^4)^3
(((z/(1+z*v))/(1+(z/(1+z*v)))))*y*((1/(1-1*u*x)))*(x-t)
2*(-1+(-1+x)/(2+x))/(2+x)^2
Factorizar el polinomio:
y^5-y^3-y+1
y^5+y+1
-y^3+y^2-1
y^3+y^2*x-3*y*x+9*x+27
Descomponer al cuadrado:
-y^4-8*y^2-8
-y^4+9*y^2-3
-y^4-8*y^2-2
-y^4+8*y^2+4
Expresiones idénticas
cos(seis *a)/(cos(tres *a)+sin(tres *a))
coseno de (6 multiplicar por a) dividir por ( coseno de (3 multiplicar por a) más seno de (3 multiplicar por a))
coseno de (seis multiplicar por a) dividir por ( coseno de (tres multiplicar por a) más seno de (tres multiplicar por a))
cos(6a)/(cos(3a)+sin(3a))
cos6a/cos3a+sin3a
cos(6*a) dividir por (cos(3*a)+sin(3*a))
Expresiones semejantes
cos(6*a)/(cos(3*a)-sin(3*a))
Expresiones con funciones
Coseno cos
cos(4*x)/(8*(cos(4*x)^2)^(3/2))
cos(2*x)*x/(cos(x)+sin(x))-cos(x)
cos(2*x)*x/(sin(x)+cos(x))
cos(106)/(sin(8)*cos(8))
cos(a+b)/((cos(a)*sin(b)))
Coseno cos
cos(4*x)/(8*(cos(4*x)^2)^(3/2))
cos(2*x)*x/(cos(x)+sin(x))-cos(x)
cos(2*x)*x/(sin(x)+cos(x))
cos(106)/(sin(8)*cos(8))
cos(a+b)/((cos(a)*sin(b)))
Seno sin
sin(7*n/(2-a))*(-7)
sin(6*pi*x)/(12*pi)+sin(8*pi*x)/(16*pi)
sin^2/(cos-1)
sin^2a(cos4a-cos2a)/(sina-2sin3a+sin5a)
sin20/(2*cos10)

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(6*a)/(cos(3*a)+sin(3*a))

¿Cómo vas a descomponer esta cos(6a)/(cos(3a)+sin(3*a)) expresión en fracciones?

Solución

Ha introducido [src]

      cos(6*a)     
-------------------
cos(3*a) + sin(3*a)

$$\frac{\cos{\left(6 a \right)}}{\sin{\left(3 a \right)} + \cos{\left(3 a \right)}}$$

cos(6*a)/(cos(3*a) + sin(3*a))

Simplificación general [src]

   ___         
 \/ 2 *cos(6*a)
---------------
     /      pi\
2*sin|3*a + --|
     \      4 /

$$\frac{\sqrt{2} \cos{\left(6 a \right)}}{2 \sin{\left(3 a + \frac{\pi}{4} \right)}}$$

sqrt(2)*cos(6*a)/(2*sin(3*a + pi/4))

Potencias [src]

              -6*I*a    6*I*a            
             e         e                 
             ------- + ------            
                2        2               
-----------------------------------------
 -3*I*a    3*I*a     /   -3*I*a    3*I*a\
e         e        I*\- e       + e     /
------- + ------ - ----------------------
   2        2                2

$$\frac{\frac{e^{6 i a}}{2} + \frac{e^{- 6 i a}}{2}}{- \frac{i \left(e^{3 i a} - e^{- 3 i a}\right)}{2} + \frac{e^{3 i a}}{2} + \frac{e^{- 3 i a}}{2}}$$

(exp(-6*i*a)/2 + exp(6*i*a)/2)/(exp(-3*i*a)/2 + exp(3*i*a)/2 - i*(-exp(-3*i*a) + exp(3*i*a))/2)

Abrimos la expresión [src]

                                                                          4                                               2                                               6                    
                        1                                           48*cos (a)                                      18*cos (a)                                      32*cos (a)                 
- --------------------------------------------- - --------------------------------------------- + --------------------------------------------- + ---------------------------------------------
         3                                 3             3                                 3             3                                 3             3                                 3   
  - 4*sin (a) - 3*cos(a) + 3*sin(a) + 4*cos (a)   - 4*sin (a) - 3*cos(a) + 3*sin(a) + 4*cos (a)   - 4*sin (a) - 3*cos(a) + 3*sin(a) + 4*cos (a)   - 4*sin (a) - 3*cos(a) + 3*sin(a) + 4*cos (a)

$$\frac{32 \cos^{6}{\left(a \right)}}{- 4 \sin^{3}{\left(a \right)} + 3 \sin{\left(a \right)} + 4 \cos^{3}{\left(a \right)} - 3 \cos{\left(a \right)}} - \frac{48 \cos^{4}{\left(a \right)}}{- 4 \sin^{3}{\left(a \right)} + 3 \sin{\left(a \right)} + 4 \cos^{3}{\left(a \right)} - 3 \cos{\left(a \right)}} + \frac{18 \cos^{2}{\left(a \right)}}{- 4 \sin^{3}{\left(a \right)} + 3 \sin{\left(a \right)} + 4 \cos^{3}{\left(a \right)} - 3 \cos{\left(a \right)}} - \frac{1}{- 4 \sin^{3}{\left(a \right)} + 3 \sin{\left(a \right)} + 4 \cos^{3}{\left(a \right)} - 3 \cos{\left(a \right)}}$$

-1/(-4*sin(a)^3 - 3*cos(a) + 3*sin(a) + 4*cos(a)^3) - 48*cos(a)^4/(-4*sin(a)^3 - 3*cos(a) + 3*sin(a) + 4*cos(a)^3) + 18*cos(a)^2/(-4*sin(a)^3 - 3*cos(a) + 3*sin(a) + 4*cos(a)^3) + 32*cos(a)^6/(-4*sin(a)^3 - 3*cos(a) + 3*sin(a) + 4*cos(a)^3)

Respuesta numérica [src]

cos(6*a)/(cos(3*a) + sin(3*a))

cos(6*a)/(cos(3*a) + sin(3*a))

Parte trigonométrica [src]

                        2                      
                 1 - tan (3*a)                 
-----------------------------------------------
                /       2/3*a\          /3*a\ \
                |1 - tan |---|     2*tan|---| |
/       2     \ |        \ 2 /          \ 2 / |
\1 + tan (3*a)/*|------------- + -------------|
                |       2/3*a\          2/3*a\|
                |1 + tan |---|   1 + tan |---||
                \        \ 2 /           \ 2 //

$$\frac{1 - \tan^{2}{\left(3 a \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{3 a}{2} \right)}}{\tan^{2}{\left(\frac{3 a}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{3 a}{2} \right)}}{\tan^{2}{\left(\frac{3 a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(3 a \right)} + 1\right)}$$

  ___             /      pi\
\/ 2 *cos(6*a)*csc|3*a + --|
                  \      4 /
----------------------------
             2

$$\frac{\sqrt{2} \cos{\left(6 a \right)} \csc{\left(3 a + \frac{\pi}{4} \right)}}{2}$$

      ___     
    \/ 2      
--------------
   /       pi\
csc|-3*a + --|
   \       4 /

$$\frac{\sqrt{2}}{\csc{\left(- 3 a + \frac{\pi}{4} \right)}}$$

                   1                    
----------------------------------------
/   1             1      \    /pi      \
|-------- + -------------|*csc|-- - 6*a|
|csc(3*a)      /pi      \|    \2       /
|           csc|-- - 3*a||              
\              \2       //

$$\frac{1}{\left(\frac{1}{\csc{\left(- 3 a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(3 a \right)}}\right) \csc{\left(- 6 a + \frac{\pi}{2} \right)}}$$

  ___    2/pi + 12*a\ /        2/pi   3*a\\
\/ 2 *sin |---------|*|-1 + cot |-- + ---||
          \    8    / \         \8     2 //

$$\sqrt{2} \left(\cot^{2}{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)} - 1\right) \sin^{2}{\left(\frac{12 a + \pi}{8} \right)}$$

  ___    2      /       2/pi   3*a\\ /       2     \
\/ 2 *cos (3*a)*|1 + tan |-- + ---||*\1 - tan (3*a)/
                \        \8     2 //                
----------------------------------------------------
                       /pi   3*a\                   
                  4*tan|-- + ---|                   
                       \8     2 /

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(3 a \right)}\right) \left(\tan^{2}{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(3 a \right)}}{4 \tan{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)}}$$

  ___    2      /        2     \    /pi   3*a\
\/ 2 *sin (3*a)*\-1 + cot (3*a)/*tan|-- + ---|
                                    \8     2 /
----------------------------------------------
                   2/pi + 12*a\               
              4*sin |---------|               
                    \    8    /

$$\frac{\sqrt{2} \left(\cot^{2}{\left(3 a \right)} - 1\right) \sin^{2}{\left(3 a \right)} \tan{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)}}{4 \sin^{2}{\left(\frac{12 a + \pi}{8} \right)}}$$

  ___    /      pi\
\/ 2 *sec|3*a - --|
         \      4 /
-------------------
     2*sec(6*a)

$$\frac{\sqrt{2} \sec{\left(3 a - \frac{\pi}{4} \right)}}{2 \sec{\left(6 a \right)}}$$

        /pi      \      
     sin|-- + 6*a|      
        \2       /      
------------------------
              /pi      \
sin(3*a) + sin|-- + 3*a|
              \2       /

$$\frac{\sin{\left(6 a + \frac{\pi}{2} \right)}}{\sin{\left(3 a \right)} + \sin{\left(3 a + \frac{\pi}{2} \right)}}$$

   ___         
 \/ 2 *cos(6*a)
---------------
     /      pi\
2*sin|3*a + --|
     \      4 /

$$\frac{\sqrt{2} \cos{\left(6 a \right)}}{2 \sin{\left(3 a + \frac{\pi}{4} \right)}}$$

        cos(6*a)        
------------------------
              /      pi\
cos(3*a) + cos|3*a - --|
              \      2 /

$$\frac{\cos{\left(6 a \right)}}{\cos{\left(3 a \right)} + \cos{\left(3 a - \frac{\pi}{2} \right)}}$$

  ___    /      pi\
\/ 2 *csc|3*a + --|
         \      4 /
-------------------
       /pi      \  
  2*csc|-- - 6*a|  
       \2       /

$$\frac{\sqrt{2} \csc{\left(3 a + \frac{\pi}{4} \right)}}{2 \csc{\left(- 6 a + \frac{\pi}{2} \right)}}$$

   ___         
 \/ 2 *cos(6*a)
---------------
     /      pi\
2*cos|3*a - --|
     \      4 /

$$\frac{\sqrt{2} \cos{\left(6 a \right)}}{2 \cos{\left(3 a - \frac{\pi}{4} \right)}}$$

  ___ /       2/pi   3*a\\
\/ 2 *|1 - tan |-- + ---||
      \        \8     2 //
--------------------------
           2/pi   3*a\    
    1 + tan |-- + ---|    
            \8     2 /

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)}\right)}{\tan^{2}{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)} + 1}$$

  ___    /      3*pi\
\/ 2 *sin|3*a + ----|
         \       4  /

$$\sqrt{2} \sin{\left(3 a + \frac{3 \pi}{4} \right)}$$

  ___             /      pi\
\/ 2 *cos(6*a)*sec|3*a - --|
                  \      4 /
----------------------------
             2

$$\frac{\sqrt{2} \cos{\left(6 a \right)} \sec{\left(3 a - \frac{\pi}{4} \right)}}{2}$$

              1               
------------------------------
/   1          1    \         
|-------- + --------|*sec(6*a)
\csc(3*a)   sec(3*a)/

$$\frac{1}{\left(\frac{1}{\sec{\left(3 a \right)}} + \frac{1}{\csc{\left(3 a \right)}}\right) \sec{\left(6 a \right)}}$$

  ___ /       2/pi   3*a\\ /        2     \
\/ 2 *|1 + cot |-- + ---||*\-1 + cot (3*a)/
      \        \8     2 //                 
-------------------------------------------
        /       2     \    /pi   3*a\      
      4*\1 + cot (3*a)/*cot|-- + ---|      
                           \8     2 /

$$\frac{\sqrt{2} \left(\cot^{2}{\left(3 a \right)} - 1\right) \left(\cot^{2}{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)} + 1\right)}{4 \left(\cot^{2}{\left(3 a \right)} + 1\right) \cot{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)}}$$

  ___    /      pi\
\/ 2 *cos|3*a + --|
         \      4 /

$$\sqrt{2} \cos{\left(3 a + \frac{\pi}{4} \right)}$$

                         2                      
                 -1 + cot (3*a)                 
------------------------------------------------
                /        2/3*a\          /3*a\ \
                |-1 + cot |---|     2*cot|---| |
/       2     \ |         \ 2 /          \ 2 / |
\1 + cot (3*a)/*|-------------- + -------------|
                |       2/3*a\           2/3*a\|
                |1 + cot |---|    1 + cot |---||
                \        \ 2 /            \ 2 //

$$\frac{\cot^{2}{\left(3 a \right)} - 1}{\left(\frac{\cot^{2}{\left(\frac{3 a}{2} \right)} - 1}{\cot^{2}{\left(\frac{3 a}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{3 a}{2} \right)}}{\cot^{2}{\left(\frac{3 a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(3 a \right)} + 1\right)}$$

  ___    /pi      \
\/ 2 *sin|-- + 6*a|
         \2       /
-------------------
       /      pi\  
  2*sin|3*a + --|  
       \      4 /

$$\frac{\sqrt{2} \sin{\left(6 a + \frac{\pi}{2} \right)}}{2 \sin{\left(3 a + \frac{\pi}{4} \right)}}$$

      ___    
    \/ 2     
-------------
   /      pi\
sec|3*a + --|
   \      4 /

$$\frac{\sqrt{2}}{\sec{\left(3 a + \frac{\pi}{4} \right)}}$$

  ___ /       2/pi   3*a\\ /       2     \
\/ 2 *|1 + tan |-- + ---||*\1 - tan (3*a)/
      \        \8     2 //                
------------------------------------------
       /       2     \    /pi   3*a\      
     4*\1 + tan (3*a)/*tan|-- + ---|      
                          \8     2 /

$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(3 a \right)}\right) \left(\tan^{2}{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)} + 1\right)}{4 \left(\tan^{2}{\left(3 a \right)} + 1\right) \tan{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)}}$$

                 1                 
-----------------------------------
/   1             1      \         
|-------- + -------------|*sec(6*a)
|sec(3*a)      /      pi\|         
|           sec|3*a - --||         
\              \      2 //

$$\frac{1}{\left(\frac{1}{\sec{\left(3 a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(3 a \right)}}\right) \sec{\left(6 a \right)}}$$

  ___ /        2/pi   3*a\\
\/ 2 *|-1 + cot |-- + ---||
      \         \8     2 //
---------------------------
            2/pi   3*a\    
     1 + cot |-- + ---|    
             \8     2 /

$$\frac{\sqrt{2} \left(\cot^{2}{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)} - 1\right)}{\cot^{2}{\left(\frac{3 a}{2} + \frac{\pi}{8} \right)} + 1}$$

sqrt(2)*(-1 + cot(pi/8 + 3*a/2)^2)/(1 + cot(pi/8 + 3*a/2)^2)

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

¿Cómo vas a descomponer esta cos(6*a)/(cos(3*a)+sin(3*a)) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta cos(6a)/(cos(3a)+sin(3*a)) expresión en fracciones?