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¿cómo vas a descomponer esta expresión en fracciones?:
(pi*a^2+pi/4)/(pi*a^2+pi/2)
sin(2*x)/(2*sin(x)-cos(x))
(x^2-3*x+2)/(x-2)
1/(x^4+1)
Factorizar el polinomio:
z^3+5*z^2+17*z+13
z^2+4*z+13
z^2/2-2*i*z
x^4+x^4
Descomponer al cuadrado:
y^4-y^2-9
x^2+x+3
y^4-y^2-8
y^4-y^2+2
Expresiones idénticas
cos(a-b)/((sin(a)*sin(b)))- uno
coseno de (a menos b) dividir por (( seno de (a) multiplicar por seno de (b))) menos 1
coseno de (a menos b) dividir por (( seno de (a) multiplicar por seno de (b))) menos uno
cos(a-b)/((sin(a)sin(b)))-1
cosa-b/sinasinb-1
cos(a-b) dividir por ((sin(a)*sin(b)))-1
Expresiones semejantes
cos(a-b)/((sin(a)*sin(b)))+1
cos(a+b)/((sin(a)*sin(b)))-1
cos(a-b)/(sin(a)*sin(b))-1
Expresiones con funciones
Coseno cos
cos(2*x)/(sin(x)-cos(x))
cos(x)/(2*sqrt(1+sin(x)))
cos^2(x)/(sin^2(x)*ctg(x))
cos(x)^2/((1+x^2)*acot(x)^2)-2*cos(x)*sin(x)/acot(x)
cos(a-b)*b/((sin(a)*sin(a)))-1
Seno sin
sin(2*x)/(2*sin(x)-cos(x))
sin(2*x)/(2*cos(2*x))
sin(x)/(2*sqrt(1-cos(x)^2)*sqrt(acos(cos(x))))
sin(6*a)/((2*sin(3*a)))
sin(5*x)/(1-cos(5*x))
Seno sin
sin(2*x)/(2*sin(x)-cos(x))
sin(2*x)/(2*cos(2*x))
sin(x)/(2*sqrt(1-cos(x)^2)*sqrt(acos(cos(x))))
sin(6*a)/((2*sin(3*a)))
sin(5*x)/(1-cos(5*x))

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(a-b)/((sin(a)*sin(b)))-1

¿Cómo vas a descomponer esta cos(a-b)/((sin(a)*sin(b)))-1 expresión en fracciones?

Solución

Ha introducido [src]

  cos(a - b)     
------------- - 1
sin(a)*sin(b)

-1 + \frac{\cos{\left(a - b \right)}}{\sin{\left(a \right)} \sin{\left(b \right)}}

cos(a - b)/((sin(a)*sin(b))) - 1

Simplificación general [src]

      1      
-------------
tan(a)*tan(b)

\frac{1}{\tan{\left(a \right)} \tan{\left(b \right)}}

1/(tan(a)*tan(b))

Respuesta numérica [src]

-1.0 + cos(a - b)/(sin(a)*sin(b))

-1.0 + cos(a - b)/(sin(a)*sin(b))

Unión de expresiones racionales [src]

-sin(a)*sin(b) + cos(a - b)
---------------------------
       sin(a)*sin(b)

\frac{- \sin{\left(a \right)} \sin{\left(b \right)} + \cos{\left(a - b \right)}}{\sin{\left(a \right)} \sin{\left(b \right)}}

(-sin(a)*sin(b) + cos(a - b))/(sin(a)*sin(b))

Denominador racional [src]

-sin(a)*sin(b) + cos(a - b)
---------------------------
       sin(a)*sin(b)

\frac{- \sin{\left(a \right)} \sin{\left(b \right)} + \cos{\left(a - b \right)}}{\sin{\left(a \right)} \sin{\left(b \right)}}

(-sin(a)*sin(b) + cos(a - b))/(sin(a)*sin(b))

Combinatoria [src]

-sin(a)*sin(b) + cos(a - b)
---------------------------
       sin(a)*sin(b)

\frac{- \sin{\left(a \right)} \sin{\left(b \right)} + \cos{\left(a - b \right)}}{\sin{\left(a \right)} \sin{\left(b \right)}}

(-sin(a)*sin(b) + cos(a - b))/(sin(a)*sin(b))

Abrimos la expresión [src]

cos(a)*cos(b)
-------------
sin(a)*sin(b)

\frac{\cos{\left(a \right)} \cos{\left(b \right)}}{\sin{\left(a \right)} \sin{\left(b \right)}}

cos(a)*cos(b)/(sin(a)*sin(b))

Potencias [src]

          / I*(a - b)    I*(b - a)\   
          |e            e         |   
        4*|---------- + ----------|   
          \    2            2     /   
-1 - ---------------------------------
     /   -I*a    I*a\ /   -I*b    I*b\
     \- e     + e   /*\- e     + e   /

-1 - \frac{4 \left(\frac{e^{i \left(- a + b\right)}}{2} + \frac{e^{i \left(a - b\right)}}{2}\right)}{\left(e^{i a} - e^{- i a}\right) \left(e^{i b} - e^{- i b}\right)}

-1 - 4*(exp(i*(a - b))/2 + exp(i*(b - a))/2)/((-exp(-i*a) + exp(i*a))*(-exp(-i*b) + exp(i*b)))

Parte trigonométrica [src]

                    /         4/a   b\\                              
                    |    4*sin |- - -||                              
                    |          \2   2/|                              
                    |1 - -------------|*sin(a)*sin(b)                
                    |        2        |                              
                    \     sin (a - b) /                              
-1 + ----------------------------------------------------------------
        /         4/a   b\\                                          
        |    4*sin |- - -||                                          
        |          \2   2/|    2/a\    2/b\    2/pi   a\    2/pi   b\
     16*|1 + -------------|*sin |-|*sin |-|*sin |-- + -|*sin |-- + -|
        |        2        |     \2/     \2/     \2    2/     \2    2/
        \     sin (a - b) /

\frac{\left(- \frac{4 \sin^{4}{\left(\frac{a}{2} - \frac{b}{2} \right)}}{\sin^{2}{\left(a - b \right)}} + 1\right) \sin{\left(a \right)} \sin{\left(b \right)}}{16 \left(\frac{4 \sin^{4}{\left(\frac{a}{2} - \frac{b}{2} \right)}}{\sin^{2}{\left(a - b \right)}} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{2}{\left(\frac{b}{2} \right)} \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} \sin^{2}{\left(\frac{b}{2} + \frac{\pi}{2} \right)}} - 1

     csc(a)*csc(b)
-1 + -------------
       sec(a - b)

\frac{\csc{\left(a \right)} \csc{\left(b \right)}}{\sec{\left(a - b \right)}} - 1

                                 2/a   pi   b\                     
                              cos |- - -- - -|                     
                                  \2   2    2/                     
                          1 - ----------------                     
                                   2/a   b\                        
                                cos |- - -|                        
                                    \2   2/                        
-1 + --------------------------------------------------------------
       /       2/a   pi   b\\                                      
       |    cos |- - -- - -||                                      
       |        \2   2    2/|    /a\    /b\    /a   pi\    /b   pi\
     4*|1 + ----------------|*cos|-|*cos|-|*cos|- - --|*cos|- - --|
       |         2/a   b\   |    \2/    \2/    \2   2 /    \2   2 /
       |      cos |- - -|   |                                      
       \          \2   2/   /

\frac{1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{b}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}}{4 \left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{b}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}\right) \cos{\left(\frac{a}{2} \right)} \cos{\left(\frac{b}{2} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \cos{\left(\frac{b}{2} - \frac{\pi}{2} \right)}} - 1

     /         2/a   b\   \                                      
     |      sec |- - -|   |                                      
     |          \2   2/   |    /a\    /b\    /a   pi\    /b   pi\
     |1 - ----------------|*sec|-|*sec|-|*sec|- - --|*sec|- - --|
     |       2/a   pi   b\|    \2/    \2/    \2   2 /    \2   2 /
     |    sec |- - -- - -||                                      
     \        \2   2    2//                                      
-1 + ------------------------------------------------------------
                         /         2/a   b\   \                  
                         |      sec |- - -|   |                  
                         |          \2   2/   |                  
                       4*|1 + ----------------|                  
                         |       2/a   pi   b\|                  
                         |    sec |- - -- - -||                  
                         \        \2   2    2//

\frac{\left(- \frac{\sec^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{b}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{a}{2} \right)} \sec{\left(\frac{b}{2} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \sec{\left(\frac{b}{2} - \frac{\pi}{2} \right)}}{4 \left(\frac{\sec^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{b}{2} - \frac{\pi}{2} \right)}} + 1\right)} - 1

       1                 1       
--------------- + ---------------
   /    pi    \      /pi        \
csc|b + -- - a|   csc|-- - a - b|
   \    2     /      \2         /
---------------------------------
       1                 1       
--------------- - ---------------
   /    pi    \      /pi        \
csc|b + -- - a|   csc|-- - a - b|
   \    2     /      \2         /

\frac{\frac{1}{\csc{\left(- a + b + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- a - b + \frac{\pi}{2} \right)}}}{\frac{1}{\csc{\left(- a + b + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(- a - b + \frac{\pi}{2} \right)}}}

                       /       2/a   b\\    /a\    /b\                  
                       |1 - tan |- - -||*cot|-|*cot|-|                  
                       \        \2   2//    \2/    \2/                  
-1 + -------------------------------------------------------------------
                                       2               2                
       /       2/a   b\\ /        2/a\\  /        2/b\\     4/a\    4/b\
     4*|1 + tan |- - -||*|-1 + cot |-|| *|-1 + cot |-|| *sin |-|*sin |-|
       \        \2   2// \         \4//  \         \4//      \4/     \4/

\frac{\left(1 - \tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}\right) \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{b}{2} \right)}}{4 \left(\tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{b}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{a}{4} \right)} \sin^{4}{\left(\frac{b}{4} \right)}} - 1

     /       2/a\\ /       2/b\\ /        2/a   b\\
     |1 + cot |-||*|1 + cot |-||*|-1 + cot |- - -||
     \        \2// \        \2// \         \2   2//
-1 + ----------------------------------------------
             /       2/a   b\\    /a\    /b\       
           4*|1 + cot |- - -||*cot|-|*cot|-|       
             \        \2   2//    \2/    \2/

\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{b}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)} - 1\right)}{4 \left(\cot^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{b}{2} \right)}} - 1

   /    pi\    /    pi\
sec|a - --|*sec|b - --|
   \    2 /    \    2 /
-----------------------
     sec(a)*sec(b)

\frac{\sec{\left(a - \frac{\pi}{2} \right)} \sec{\left(b - \frac{\pi}{2} \right)}}{\sec{\left(a \right)} \sec{\left(b \right)}}

                          2              2                          
             /       2/a\\  /       2/b\\  /       2/a   b\\        
             |1 + tan |-|| *|1 + tan |-|| *|1 - tan |- - -||        
             \        \4//  \        \4//  \        \2   2//        
-1 + ---------------------------------------------------------------
                                      2              2              
       /       2/a   b\\ /       2/a\\  /       2/b\\     /a\    /b\
     4*|1 + tan |- - -||*|1 - tan |-|| *|1 - tan |-|| *tan|-|*tan|-|
       \        \2   2// \        \4//  \        \4//     \2/    \2/

-1 + \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{b}{4} \right)} + 1\right)^{2}}{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{b}{4} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{b}{2} \right)}}

      1      
-------------
tan(a)*tan(b)

\frac{1}{\tan{\left(a \right)} \tan{\left(b \right)}}

    /        pi\      /    pi    \ 
 sin|a + b + --| + sin|a + -- - b| 
    \        2 /      \    2     / 
-----------------------------------
     /        pi\      /    pi    \
- sin|a + b + --| + sin|a + -- - b|
     \        2 /      \    2     /

\frac{\sin{\left(a - b + \frac{\pi}{2} \right)} + \sin{\left(a + b + \frac{\pi}{2} \right)}}{\sin{\left(a - b + \frac{\pi}{2} \right)} - \sin{\left(a + b + \frac{\pi}{2} \right)}}

     cos(a)*cos(b)     
-----------------------
   /    pi\    /    pi\
cos|a - --|*cos|b - --|
   \    2 /    \    2 /

\frac{\cos{\left(a \right)} \cos{\left(b \right)}}{\cos{\left(a - \frac{\pi}{2} \right)} \cos{\left(b - \frac{\pi}{2} \right)}}

     csc(a)*csc(b)     
-----------------------
   /pi    \    /pi    \
csc|-- - a|*csc|-- - b|
   \2     /    \2     /

\frac{\csc{\left(a \right)} \csc{\left(b \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(- b + \frac{\pi}{2} \right)}}

                             2/a   b\                 
                      1 - tan |- - -|                 
                              \2   2/                 
-1 + -------------------------------------------------
       /       2/a   b\\    2/a\    2/b\    /a\    /b\
     4*|1 + tan |- - -||*cos |-|*cos |-|*tan|-|*tan|-|
       \        \2   2//     \2/     \2/    \2/    \2/

\frac{1 - \tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}{4 \left(\tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)} + 1\right) \cos^{2}{\left(\frac{a}{2} \right)} \cos^{2}{\left(\frac{b}{2} \right)} \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{b}{2} \right)}} - 1

     /       2/a\\ /       2/b\\ /       2/a   b\\
     |1 + tan |-||*|1 + tan |-||*|1 - tan |- - -||
     \        \2// \        \2// \        \2   2//
-1 + ---------------------------------------------
             /       2/a   b\\    /a\    /b\      
           4*|1 + tan |- - -||*tan|-|*tan|-|      
             \        \2   2//    \2/    \2/

\frac{\left(1 - \tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{b}{2} \right)} + 1\right)}{4 \left(\tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{b}{2} \right)}} - 1

     /       2/pi   b   a\\                                      
     |    csc |-- + - - -||                                      
     |        \2    2   2/|    /a\    /b\    /pi   a\    /pi   b\
     |1 - ----------------|*csc|-|*csc|-|*csc|-- - -|*csc|-- - -|
     |         2/a   b\   |    \2/    \2/    \2    2/    \2    2/
     |      csc |- - -|   |                                      
     \          \2   2/   /                                      
-1 + ------------------------------------------------------------
                         /       2/pi   b   a\\                  
                         |    csc |-- + - - -||                  
                         |        \2    2   2/|                  
                       4*|1 + ----------------|                  
                         |         2/a   b\   |                  
                         |      csc |- - -|   |                  
                         \          \2   2/   /

\frac{\left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{b}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}\right) \csc{\left(\frac{a}{2} \right)} \csc{\left(\frac{b}{2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)} \csc{\left(- \frac{b}{2} + \frac{\pi}{2} \right)}}{4 \left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{b}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}\right)} - 1

                                            2/a   b\                                
                                     1 - tan |- - -|                                
                                             \2   2/                                
-1 + -------------------------------------------------------------------------------
                                      2              2                              
       /       2/a   b\\ /       2/a\\  /       2/b\\     4/a\    4/b\    /a\    /b\
     4*|1 + tan |- - -||*|1 - tan |-|| *|1 - tan |-|| *cos |-|*cos |-|*tan|-|*tan|-|
       \        \2   2// \        \4//  \        \4//      \4/     \4/    \2/    \2/

-1 + \frac{1 - \tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{b}{4} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)} + 1\right) \cos^{4}{\left(\frac{a}{4} \right)} \cos^{4}{\left(\frac{b}{4} \right)} \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{b}{2} \right)}}

            cos(a - b)      
-1 + -----------------------
        /    pi\    /    pi\
     cos|a - --|*cos|b - --|
        \    2 /    \    2 /

-1 + \frac{\cos{\left(a - b \right)}}{\cos{\left(a - \frac{\pi}{2} \right)} \cos{\left(b - \frac{\pi}{2} \right)}}

cot(a)*cot(b)

\cot{\left(a \right)} \cot{\left(b \right)}

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

\frac{\csc{\left(a \right)} \csc{\left(b \right)}}{\csc{\left(- a + b + \frac{\pi}{2} \right)}} - 1

       2/a   b\          2/a   b\
1 - tan |- + -|   1 - tan |- - -|
        \2   2/           \2   2/
--------------- + ---------------
       2/a   b\          2/a   b\
1 + tan |- + -|   1 + tan |- - -|
        \2   2/           \2   2/
---------------------------------
       2/a   b\          2/a   b\
1 - tan |- - -|   1 - tan |- + -|
        \2   2/           \2   2/
--------------- - ---------------
       2/a   b\          2/a   b\
1 + tan |- - -|   1 + tan |- + -|
        \2   2/           \2   2/

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

                        /         4/a - b\\                                 
                        |    4*sin |-----||                                 
                        |          \  2  /|                                 
                        |1 - -------------|*sin(a)*sin(b)                   
                        |        2        |                                 
                        \     sin (a - b) /                                 
-1 + -----------------------------------------------------------------------
                               /         4/a - b\\                          
                               |    4*sin |-----||                          
                               |          \  2  /|                          
     (1 - cos(a))*(1 - cos(b))*|1 + -------------|*(1 + cos(a))*(1 + cos(b))
                               |        2        |                          
                               \     sin (a - b) /

-1 + \frac{\left(- \frac{4 \sin^{4}{\left(\frac{a - b}{2} \right)}}{\sin^{2}{\left(a - b \right)}} + 1\right) \sin{\left(a \right)} \sin{\left(b \right)}}{\left(1 - \cos{\left(a \right)}\right) \left(1 - \cos{\left(b \right)}\right) \left(\frac{4 \sin^{4}{\left(\frac{a - b}{2} \right)}}{\sin^{2}{\left(a - b \right)}} + 1\right) \left(\cos{\left(a \right)} + 1\right) \left(\cos{\left(b \right)} + 1\right)}

                  2              2                                
     /       2/a\\  /       2/b\\  /         1     \    /a\    /b\
     |1 + cot |-|| *|1 + cot |-|| *|1 - -----------|*cot|-|*cot|-|
     \        \4//  \        \4//  |       2/a   b\|    \2/    \2/
                                   |    cot |- - -||              
                                   \        \2   2//              
-1 + -------------------------------------------------------------
                                            2               2     
            /         1     \ /        2/a\\  /        2/b\\      
          4*|1 + -----------|*|-1 + cot |-|| *|-1 + cot |-||      
            |       2/a   b\| \         \4//  \         \4//      
            |    cot |- - -||                                     
            \        \2   2//

\frac{\left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{b}{4} \right)} + 1\right)^{2} \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{b}{2} \right)}}{4 \left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} - \frac{b}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{b}{4} \right)} - 1\right)^{2}} - 1

cos(a + b) + cos(a - b) 
------------------------
-cos(a + b) + cos(a - b)

\frac{\cos{\left(a - b \right)} + \cos{\left(a + b \right)}}{\cos{\left(a - b \right)} - \cos{\left(a + b \right)}}

        /    pi    \
     sin|a + -- - b|
        \    2     /
-1 + ---------------
      sin(a)*sin(b)

-1 + \frac{\sin{\left(a - b + \frac{\pi}{2} \right)}}{\sin{\left(a \right)} \sin{\left(b \right)}}

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

\frac{\sec{\left(a - \frac{\pi}{2} \right)} \sec{\left(b - \frac{\pi}{2} \right)}}{\sec{\left(a - b \right)}} - 1

        2/a   b\           2/a   b\
-1 + cot |- + -|   -1 + cot |- - -|
         \2   2/            \2   2/
---------------- + ----------------
       2/a   b\           2/a   b\ 
1 + cot |- + -|    1 + cot |- - -| 
        \2   2/            \2   2/ 
-----------------------------------
        2/a   b\           2/a   b\
-1 + cot |- - -|   -1 + cot |- + -|
         \2   2/            \2   2/
---------------- - ----------------
       2/a   b\           2/a   b\ 
1 + cot |- - -|    1 + cot |- + -| 
        \2   2/            \2   2/

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

sin(2*a)*sin(2*b)
-----------------
     2       2   
4*sin (a)*sin (b)

\frac{\sin{\left(2 a \right)} \sin{\left(2 b \right)}}{4 \sin^{2}{\left(a \right)} \sin^{2}{\left(b \right)}}

    1            1     
---------- + ----------
sec(a + b)   sec(a - b)
-----------------------
    1            1     
---------- - ----------
sec(a - b)   sec(a + b)

\frac{\frac{1}{\sec{\left(a + b \right)}} + \frac{1}{\sec{\left(a - b \right)}}}{- \frac{1}{\sec{\left(a + b \right)}} + \frac{1}{\sec{\left(a - b \right)}}}

(1/sec(a + b) + 1/sec(a - b))/(1/sec(a - b) - 1/sec(a + b))

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¿Cómo vas a descomponer esta cos(a-b)/((sin(a)*sin(b)))-1 expresión en fracciones?

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