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Expresiones semejantes
sin(a)*(-cot(a))*tan(180*pi/(360-a))/(-cos(a))
sin(a)*(cot(a))*tan(180*pi/(360+a))/(-cos(a))
sin(a)*(-cot(a))*tan(180*pi/(360+a))/(cos(a))
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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(a)*(-cot(a))*tan(180*pi/(360+a))/(-cos(a))

¿Cómo vas a descomponer esta sin(a)(-cot(a))tan(180*pi/(360+a))/(-cos(a)) expresión en fracciones?

Solución

Ha introducido [src]

                    / 180*pi\
sin(a)*(-cot(a))*tan|-------|
                    \360 + a/
-----------------------------
           -cos(a)

$$\frac{\sin{\left(a \right)} \left(- \cot{\left(a \right)}\right) \tan{\left(\frac{180 \pi}{a + 360} \right)}}{\left(-1\right) \cos{\left(a \right)}}$$

((sin(a)*(-cot(a)))*tan((180*pi)/(360 + a)))/((-cos(a)))

Simplificación general [src]

   / 180*pi\
tan|-------|
   \360 + a/

$$\tan{\left(\frac{180 \pi}{a + 360} \right)}$$

tan(180*pi/(360 + a))

Respuesta numérica [src]

cot(a)*sin(a)*tan((180*pi)/(360 + a))/cos(a)

cot(a)*sin(a)*tan((180*pi)/(360 + a))/cos(a)

Denominador racional [src]

                 / 180*pi\
cot(a)*sin(a)*tan|-------|
                 \360 + a/
--------------------------
          cos(a)

$$\frac{\sin{\left(a \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$

cot(a)*sin(a)*tan(180*pi/(360 + a))/cos(a)

Unión de expresiones racionales [src]

                 / 180*pi\
cot(a)*sin(a)*tan|-------|
                 \360 + a/
--------------------------
          cos(a)

$$\frac{\sin{\left(a \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$

cot(a)*sin(a)*tan(180*pi/(360 + a))/cos(a)

Combinatoria [src]

                 / 180*pi\
cot(a)*sin(a)*tan|-------|
                 \360 + a/
--------------------------
          cos(a)

$$\frac{\sin{\left(a \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$

cot(a)*sin(a)*tan(180*pi/(360 + a))/cos(a)

Potencias [src]

                  /   180*pi*I    -180*pi*I\        
                  |   --------    ---------|        
 /   -I*a    I*a\ |   360 + a      360 + a |        
-\- e     + e   /*\- e         + e         /*cot(a) 
----------------------------------------------------
                       / -180*pi*I    180*pi*I\     
      /   I*a    -I*a\ | ---------    --------|     
      |  e      e    | |  360 + a     360 + a |     
    2*|- ---- - -----|*\e          + e        /     
      \   2       2  /

$$- \frac{\left(e^{i a} - e^{- i a}\right) \left(- e^{\frac{180 i \pi}{a + 360}} + e^{- \frac{180 i \pi}{a + 360}}\right) \cot{\left(a \right)}}{2 \left(- \frac{e^{i a}}{2} - \frac{e^{- i a}}{2}\right) \left(e^{\frac{180 i \pi}{a + 360}} + e^{- \frac{180 i \pi}{a + 360}}\right)}$$

                 / 180*pi\
cot(a)*sin(a)*tan|-------|
                 \360 + a/
--------------------------
          cos(a)

$$\frac{\sin{\left(a \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$

cot(a)*sin(a)*tan(180*pi/(360 + a))/cos(a)

Denominador común [src]

                 / 180*pi\
cot(a)*sin(a)*tan|-------|
                 \360 + a/
--------------------------
          cos(a)

$$\frac{\sin{\left(a \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$

cot(a)*sin(a)*tan(180*pi/(360 + a))/cos(a)

Abrimos la expresión [src]

                 / 180*pi\
cot(a)*sin(a)*tan|-------|
                 \360 + a/
--------------------------
          cos(a)

$$\frac{\sin{\left(a \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$

cot(a)*sin(a)*tan((180*pi)/(360 + a))/cos(a)

Compilar la expresión [src]

                 / 180*pi\
cot(a)*sin(a)*tan|-------|
                 \360 + a/
--------------------------
          cos(a)

$$\frac{\sin{\left(a \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$

cot(a)*sin(a)*tan((180*pi)/(360 + a))/cos(a)

Parte trigonométrica [src]

             2*cot(a)            
---------------------------------
/       1   \    /a\    / 180*pi\
|1 - -------|*cot|-|*cot|-------|
|       2/a\|    \2/    \360 + a/
|    cot |-||                    
\        \2//

$$\frac{2 \cot{\left(a \right)}}{\left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{180 \pi}{a + 360} \right)}}$$

            /a\    / 180*pi\
2*cot(a)*cot|-|*tan|-------|
            \2/    \360 + a/
----------------------------
                2/a\        
        -1 + cot |-|        
                 \2/

$$\frac{2 \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} - 1}$$

                   / 180*pi\               
                sin|-------|               
                   \360 + a/               
-------------------------------------------
                         2                 
       /       / 90*pi \\         / 90*pi \
-3 + 2*|1 - cos|-------||  + 4*cos|-------|
       \       \360 + a//         \360 + a/

$$\frac{\sin{\left(\frac{180 \pi}{a + 360} \right)}}{2 \left(1 - \cos{\left(\frac{90 \pi}{a + 360} \right)}\right)^{2} + 4 \cos{\left(\frac{90 \pi}{a + 360} \right)} - 3}$$

/       1   \    / 180*pi\
|-1 + ------|*tan|-------|
\     cos(a)/    \360 + a/
--------------------------
                /a\       
      tan(a)*tan|-|       
                \2/

$$\frac{\left(-1 + \frac{1}{\cos{\left(a \right)}}\right) \tan{\left(\frac{180 \pi}{a + 360} \right)}}{\tan{\left(\frac{a}{2} \right)} \tan{\left(a \right)}}$$

                                     / 90*pi \                               
                                2*tan|-------|                               
                                     \360 + a/                               
-----------------------------------------------------------------------------
                    /                              2                        \
                    |       /           2/ 45*pi \\      /       2/ 45*pi \\|
                    |       |    1 - tan |-------||    4*|1 - tan |-------|||
/       2/ 90*pi \\ |       |            \360 + a/|      \        \360 + a//|
|1 + tan |-------||*|-3 + 2*|1 - -----------------|  + ---------------------|
\        \360 + a// |       |           2/ 45*pi \|             2/ 45*pi \  |
                    |       |    1 + tan |-------||      1 + tan |-------|  |
                    \       \            \360 + a//              \360 + a/  /

$$\frac{2 \tan{\left(\frac{90 \pi}{a + 360} \right)}}{\left(\tan^{2}{\left(\frac{90 \pi}{a + 360} \right)} + 1\right) \left(\frac{4 \left(1 - \tan^{2}{\left(\frac{45 \pi}{a + 360} \right)}\right)}{\tan^{2}{\left(\frac{45 \pi}{a + 360} \right)} + 1} + 2 \left(- \frac{1 - \tan^{2}{\left(\frac{45 \pi}{a + 360} \right)}}{\tan^{2}{\left(\frac{45 \pi}{a + 360} \right)} + 1} + 1\right)^{2} - 3\right)}$$

       2/a\    2/ 180*pi\           
  4*sin |-|*sin |-------|*sin(2*a)  
        \2/     \360 + a/           
------------------------------------
/         4/a\\                     
|    4*sin |-||                     
|          \2/|    3       / 360*pi\
|1 - ---------|*sin (a)*sin|-------|
|        2    |            \360 + a/
\     sin (a) /

$$\frac{4 \sin^{2}{\left(\frac{a}{2} \right)} \sin{\left(2 a \right)} \sin^{2}{\left(\frac{180 \pi}{a + 360} \right)}}{\left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \sin^{3}{\left(a \right)} \sin{\left(\frac{360 \pi}{a + 360} \right)}}$$

                      /a\    /  pi    180*pi\           
          2*cos(a)*cos|-|*cos|- -- + -------|           
                      \2/    \  2    360 + a/           
--------------------------------------------------------
/          2/a\   \                                     
|       cos |-|   |                                     
|           \2/   |    / 180*pi\    /    pi\    /a   pi\
|-1 + ------------|*cos|-------|*cos|a - --|*cos|- - --|
|        2/a   pi\|    \360 + a/    \    2 /    \2   2 /
|     cos |- - --||                                     
\         \2   2 //

$$\frac{2 \cos{\left(\frac{a}{2} \right)} \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{180 \pi}{a + 360} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right) \cos{\left(\frac{180 \pi}{a + 360} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}$$

            /a\    / 180*pi\
2*cot(a)*tan|-|*tan|-------|
            \2/    \360 + a/
----------------------------
               2/a\         
        1 - tan |-|         
                \2/

$$\frac{2 \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)} \cot{\left(a \right)}}{1 - \tan^{2}{\left(\frac{a}{2} \right)}}$$

                        / 180*pi\                    
                     sin|-------|                    
                        \360 + a/                    
-----------------------------------------------------
                              2                      
       /       /pi    90*pi \\         /pi    90*pi \
-3 + 2*|1 - sin|-- + -------||  + 4*sin|-- + -------|
       \       \2    360 + a//         \2    360 + a/

$$\frac{\sin{\left(\frac{180 \pi}{a + 360} \right)}}{2 \left(1 - \sin{\left(\frac{\pi}{2} + \frac{90 \pi}{a + 360} \right)}\right)^{2} + 4 \sin{\left(\frac{\pi}{2} + \frac{90 \pi}{a + 360} \right)} - 3}$$

              2/ 180*pi\                    
           sin |-------|*sin(2*a)           
               \360 + a/                    
--------------------------------------------
/         2    \                            
|      sin (a) |           2/a\    / 360*pi\
|-1 + ---------|*sin(a)*sin |-|*sin|-------|
|          4/a\|            \2/    \360 + a/
|     4*sin |-||                            
\           \2//

$$\frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{180 \pi}{a + 360} \right)}}{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin{\left(a \right)} \sin{\left(\frac{360 \pi}{a + 360} \right)}}$$

                                1                                 
------------------------------------------------------------------
/                              2                    \             
|       /            1        \            4        |    / 180*pi\
|-3 + 2*|1 - -----------------|  + -----------------|*csc|-------|
|       |       /pi    90*pi \|       /pi    90*pi \|    \360 + a/
|       |    csc|-- - -------||    csc|-- - -------||             
\       \       \2    360 + a//       \2    360 + a//

$$\frac{1}{\left(2 \left(1 - \frac{1}{\csc{\left(\frac{\pi}{2} - \frac{90 \pi}{a + 360} \right)}}\right)^{2} - 3 + \frac{4}{\csc{\left(\frac{\pi}{2} - \frac{90 \pi}{a + 360} \right)}}\right) \csc{\left(\frac{180 \pi}{a + 360} \right)}}$$

     1      
------------
   / 180*pi\
cot|-------|
   \360 + a/

$$\frac{1}{\cot{\left(\frac{180 \pi}{a + 360} \right)}}$$

            /a\    / 180*pi\    /a\    / 180*pi\
2*cos(a)*sec|-|*sec|-------|*sin|-|*sin|-------|
            \2/    \360 + a/    \2/    \360 + a/
------------------------------------------------
              /       2/a\\                     
              |1 - tan |-||*sin(a)              
              \        \2//

$$\frac{2 \sin{\left(\frac{a}{2} \right)} \sin{\left(\frac{180 \pi}{a + 360} \right)} \cos{\left(a \right)} \sec{\left(\frac{a}{2} \right)} \sec{\left(\frac{180 \pi}{a + 360} \right)}}{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \sin{\left(a \right)}}$$

        2/ 180*pi\             
     sin |-------|*sin(2*a)    
         \360 + a/             
-------------------------------
          / 360*pi\    /    pi\
sin(a)*sin|-------|*sin|a + --|
          \360 + a/    \    2 /

$$\frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{180 \pi}{a + 360} \right)}}{\sin{\left(a \right)} \sin{\left(\frac{360 \pi}{a + 360} \right)} \sin{\left(a + \frac{\pi}{2} \right)}}$$

                  /pi   a\    /pi    180*pi\      
      2*csc(a)*csc|-- - -|*csc|-- - -------|      
                  \2    2/    \2    360 + a/      
--------------------------------------------------
/       2/pi   a\\                                
|    csc |-- - -||                                
|        \2    2/|    /a\    / 180*pi\    /pi    \
|1 - ------------|*csc|-|*csc|-------|*csc|-- - a|
|         2/a\   |    \2/    \360 + a/    \2     /
|      csc |-|   |                                
\          \2/   /

$$\frac{2 \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{180 \pi}{a + 360} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(\frac{a}{2} \right)} \csc{\left(\frac{180 \pi}{a + 360} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}$$

            / 180*pi\       
       2*tan|-------|       
            \360 + a/       
----------------------------
/        1   \           /a\
|-1 + -------|*tan(a)*tan|-|
|        2/a\|           \2/
|     tan |-||              
\         \2//

$$\frac{2 \tan{\left(\frac{180 \pi}{a + 360} \right)}}{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{a}{2} \right)} \tan{\left(a \right)}}$$

/  1        1   \    / 180*pi\
|------ - ------|*tan|-------|
\sin(a)   tan(a)/    \360 + a/
------------------------------
               /a\            
            tan|-|            
               \2/

$$\frac{\left(- \frac{1}{\tan{\left(a \right)}} + \frac{1}{\sin{\left(a \right)}}\right) \tan{\left(\frac{180 \pi}{a + 360} \right)}}{\tan{\left(\frac{a}{2} \right)}}$$

       / 180*pi\   
    sec|-------|   
       \360 + a/   
-------------------
   /  pi    180*pi\
sec|- -- + -------|
   \  2    360 + a/

$$\frac{\sec{\left(\frac{180 \pi}{a + 360} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{180 \pi}{a + 360} \right)}}$$

               /  pi    180*pi\            
            cos|- -- + -------|            
               \  2    360 + a/            
-------------------------------------------
                         2                 
       /       / 90*pi \\         / 90*pi \
-3 + 2*|1 - cos|-------||  + 4*cos|-------|
       \       \360 + a//         \360 + a/

$$\frac{\cos{\left(- \frac{\pi}{2} + \frac{180 \pi}{a + 360} \right)}}{2 \left(1 - \cos{\left(\frac{90 \pi}{a + 360} \right)}\right)^{2} + 4 \cos{\left(\frac{90 \pi}{a + 360} \right)} - 3}$$

                 /a\    / 180*pi\    /    pi\            
            2*sec|-|*sec|-------|*sec|a - --|            
                 \2/    \360 + a/    \    2 /            
---------------------------------------------------------
/         2/a\   \                                       
|      sec |-|   |                                       
|          \2/   |           /a   pi\    /  pi    180*pi\
|1 - ------------|*sec(a)*sec|- - --|*sec|- -- + -------|
|       2/a   pi\|           \2   2 /    \  2    360 + a/
|    sec |- - --||                                       
\        \2   2 //

$$\frac{2 \sec{\left(\frac{a}{2} \right)} \sec{\left(\frac{180 \pi}{a + 360} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{180 \pi}{a + 360} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$

     2/ 180*pi\
2*sin |-------|
      \360 + a/
---------------
     / 360*pi\ 
  sin|-------| 
     \360 + a/

$$\frac{2 \sin^{2}{\left(\frac{180 \pi}{a + 360} \right)}}{\sin{\left(\frac{360 \pi}{a + 360} \right)}}$$

   / 180*pi\
tan|-------|
   \360 + a/

$$\tan{\left(\frac{180 \pi}{a + 360} \right)}$$

                  2/ 180*pi\                     
             2*sin |-------|*sin(2*a)            
                   \360 + a/                     
-------------------------------------------------
             /         2    \                    
             |      sin (a) |           / 360*pi\
(1 - cos(a))*|-1 + ---------|*sin(a)*sin|-------|
             |          4/a\|           \360 + a/
             |     4*sin |-||                    
             \           \2//

$$\frac{2 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{180 \pi}{a + 360} \right)}}{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(1 - \cos{\left(a \right)}\right) \sin{\left(a \right)} \sin{\left(\frac{360 \pi}{a + 360} \right)}}$$

             / 180*pi\    /    pi\    /a   pi\       
        2*sec|-------|*sec|a - --|*sec|- - --|       
             \360 + a/    \    2 /    \2   2 /       
-----------------------------------------------------
/        2/a   pi\\                                  
|     sec |- - --||                                  
|         \2   2 /|           /a\    /  pi    180*pi\
|-1 + ------------|*sec(a)*sec|-|*sec|- -- + -------|
|          2/a\   |           \2/    \  2    360 + a/
|       sec |-|   |                                  
\           \2/   /

$$\frac{2 \sec{\left(\frac{180 \pi}{a + 360} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\left(-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \sec{\left(\frac{a}{2} \right)} \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{180 \pi}{a + 360} \right)}}$$

     2/ 180*pi\           
  sin |-------|*sin(2*a)  
      \360 + a/           
--------------------------
                 / 360*pi\
cos(a)*sin(a)*sin|-------|
                 \360 + a/

$$\frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{180 \pi}{a + 360} \right)}}{\sin{\left(a \right)} \sin{\left(\frac{360 \pi}{a + 360} \right)} \cos{\left(a \right)}}$$

                       /a\    /pi    180*pi\            
           2*csc(a)*csc|-|*csc|-- - -------|            
                       \2/    \2    360 + a/            
--------------------------------------------------------
/          2/a\   \                                     
|       csc |-|   |                                     
|           \2/   |    / 180*pi\    /pi    \    /pi   a\
|-1 + ------------|*csc|-------|*csc|-- - a|*csc|-- - -|
|        2/pi   a\|    \360 + a/    \2     /    \2    2/
|     csc |-- - -||                                     
\         \2    2//

$$\frac{2 \csc{\left(\frac{a}{2} \right)} \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{180 \pi}{a + 360} \right)}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1\right) \csc{\left(\frac{180 \pi}{a + 360} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}$$

     /a\    / 180*pi\
2*tan|-|*tan|-------|
     \2/    \360 + a/
---------------------
 /       2/a\\       
 |1 - tan |-||*tan(a)
 \        \2//

$$\frac{2 \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)}}{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \tan{\left(a \right)}}$$

                 /a   pi\    /  pi    180*pi\     
     2*cos(a)*cos|- - --|*cos|- -- + -------|     
                 \2   2 /    \  2    360 + a/     
--------------------------------------------------
/       2/a   pi\\                                
|    cos |- - --||                                
|        \2   2 /|    /a\    / 180*pi\    /    pi\
|1 - ------------|*cos|-|*cos|-------|*cos|a - --|
|         2/a\   |    \2/    \360 + a/    \    2 /
|      cos |-|   |                                
\          \2/   /

$$\frac{2 \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{180 \pi}{a + 360} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos{\left(\frac{a}{2} \right)} \cos{\left(\frac{180 \pi}{a + 360} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}$$

                               1                               
---------------------------------------------------------------
/                         2               \                    
|       /         1      \         4      |    /  pi    180*pi\
|-3 + 2*|1 - ------------|  + ------------|*sec|- -- + -------|
|       |       / 90*pi \|       / 90*pi \|    \  2    360 + a/
|       |    sec|-------||    sec|-------||                    
\       \       \360 + a//       \360 + a//

$$\frac{1}{\left(2 \left(1 - \frac{1}{\sec{\left(\frac{90 \pi}{a + 360} \right)}}\right)^{2} - 3 + \frac{4}{\sec{\left(\frac{90 \pi}{a + 360} \right)}}\right) \sec{\left(- \frac{\pi}{2} + \frac{180 \pi}{a + 360} \right)}}$$

   /  pi    180*pi\
cos|- -- + -------|
   \  2    360 + a/
-------------------
       / 180*pi\   
    cos|-------|   
       \360 + a/

$$\frac{\cos{\left(- \frac{\pi}{2} + \frac{180 \pi}{a + 360} \right)}}{\cos{\left(\frac{180 \pi}{a + 360} \right)}}$$

                                      / 90*pi \                                
                                 2*cot|-------|                                
                                      \360 + a/                                
-------------------------------------------------------------------------------
                    /                               2                         \
                    |       /            2/ 45*pi \\      /        2/ 45*pi \\|
                    |       |    -1 + cot |-------||    4*|-1 + cot |-------|||
/       2/ 90*pi \\ |       |             \360 + a/|      \         \360 + a//|
|1 + cot |-------||*|-3 + 2*|1 - ------------------|  + ----------------------|
\        \360 + a// |       |           2/ 45*pi \ |             2/ 45*pi \   |
                    |       |    1 + cot |-------| |      1 + cot |-------|   |
                    \       \            \360 + a/ /              \360 + a/   /

$$\frac{2 \cot{\left(\frac{90 \pi}{a + 360} \right)}}{\left(\cot^{2}{\left(\frac{90 \pi}{a + 360} \right)} + 1\right) \left(2 \left(- \frac{\cot^{2}{\left(\frac{45 \pi}{a + 360} \right)} - 1}{\cot^{2}{\left(\frac{45 \pi}{a + 360} \right)} + 1} + 1\right)^{2} + \frac{4 \left(\cot^{2}{\left(\frac{45 \pi}{a + 360} \right)} - 1\right)}{\cot^{2}{\left(\frac{45 \pi}{a + 360} \right)} + 1} - 3\right)}$$

/  1        1   \    /a\    / 180*pi\
|------ + ------|*tan|-|*tan|-------|
\sin(a)   tan(a)/    \2/    \360 + a/

$$\left(\frac{1}{\tan{\left(a \right)}} + \frac{1}{\sin{\left(a \right)}}\right) \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{180 \pi}{a + 360} \right)}$$

   /pi    180*pi\
csc|-- - -------|
   \2    360 + a/
-----------------
      / 180*pi\  
   csc|-------|  
      \360 + a/

$$\frac{\csc{\left(\frac{\pi}{2} - \frac{180 \pi}{a + 360} \right)}}{\csc{\left(\frac{180 \pi}{a + 360} \right)}}$$

   / 180*pi\
sec|-------|
   \360 + a/
------------
   / 180*pi\
csc|-------|
   \360 + a/

$$\frac{\sec{\left(\frac{180 \pi}{a + 360} \right)}}{\csc{\left(\frac{180 \pi}{a + 360} \right)}}$$

                / 180*pi\            
             sin|-------|            
                \360 + a/            
-------------------------------------
          / 90*pi \        4/ 45*pi \
-3 + 4*cos|-------| + 8*sin |-------|
          \360 + a/         \360 + a/

$$\frac{\sin{\left(\frac{180 \pi}{a + 360} \right)}}{8 \sin^{4}{\left(\frac{45 \pi}{a + 360} \right)} + 4 \cos{\left(\frac{90 \pi}{a + 360} \right)} - 3}$$

   / 180*pi\
sin|-------|
   \360 + a/
------------
   / 180*pi\
cos|-------|
   \360 + a/

$$\frac{\sin{\left(\frac{180 \pi}{a + 360} \right)}}{\cos{\left(\frac{180 \pi}{a + 360} \right)}}$$

                  /a\      
      2*cot(a)*cot|-|      
                  \2/      
---------------------------
/        2/a\\    / 180*pi\
|-1 + cot |-||*cot|-------|
\         \2//    \360 + a/

$$\frac{2 \cot{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \cot{\left(\frac{180 \pi}{a + 360} \right)}}$$

2*cot(a)*cot(a/2)/((-1 + cot(a/2)^2)*cot(180*pi/(360 + a)))