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How do you sin^(-1)(sin((9pi)/(8))) in partial fractions?

An expression to simplify:

The solution

You have entered [src]
      1       
--------------
   /   /9*pi\\
sin|sin|----||
   \   \ 8  //
$$\frac{1}{\sin{\left(\sin{\left(\frac{9 \pi}{8} \right)} \right)}}$$
1/sin(sin((9*pi)/8))
General simplification [src]
         -1          
---------------------
   /     ___________\
   |    /       ___ |
   |   /  1   \/ 2  |
sin|  /   - - ----- |
   \\/    2     4   /
$$- \frac{1}{\sin{\left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \right)}}$$
-1/sin(sqrt(1/2 - sqrt(2)/4))
Fraction decomposition [src]
-1/sin(sqrt(1/2 - sqrt(2)/4))
$$- \frac{1}{\sin{\left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \right)}}$$
         -1          
---------------------
   /     ___________\
   |    /       ___ |
   |   /  1   \/ 2  |
sin|  /   - - ----- |
   \\/    2     4   /
Numerical answer [src]
-2.67801330406728
-2.67801330406728
Combining rational expressions [src]
         -1          
---------------------
   /     ___________\
   |    /       ___ |
   |   /  1   \/ 2  |
sin|  /   - - ----- |
   \\/    2     4   /
$$- \frac{1}{\sin{\left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \right)}}$$
-1/sin(sqrt(1/2 - sqrt(2)/4))
Rational denominator [src]
         -1          
---------------------
   /     ___________\
   |    /       ___ |
   |   /  1   \/ 2  |
sin|  /   - - ----- |
   \\/    2     4   /
$$- \frac{1}{\sin{\left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \right)}}$$
-1/sin(sqrt(1/2 - sqrt(2)/4))
Combinatorics [src]
         -1          
---------------------
   /     ___________\
   |    /       ___ |
   |   /  1   \/ 2  |
sin|  /   - - ----- |
   \\/    2     4   /
$$- \frac{1}{\sin{\left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \right)}}$$
-1/sin(sqrt(1/2 - sqrt(2)/4))
Powers [src]
                    2*I                    
-------------------------------------------
    7*pi*I    -7*pi*I     -7*pi*I    7*pi*I
    ------    -------     -------    ------
      8          8           8         8   
   e         e           e          e      
   ------- - --------    -------- - -------
      2         2           2          2   
- e                   + e                  
$$\frac{2 i}{- e^{\frac{e^{\frac{7 i \pi}{8}}}{2} - \frac{e^{- \frac{7 i \pi}{8}}}{2}} + e^{\frac{e^{- \frac{7 i \pi}{8}}}{2} - \frac{e^{\frac{7 i \pi}{8}}}{2}}}$$
         -1          
---------------------
   /     ___________\
   |    /       ___ |
   |   /  1   \/ 2  |
sin|  /   - - ----- |
   \\/    2     4   /
$$- \frac{1}{\sin{\left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \right)}}$$
-1/sin(sqrt(1/2 - sqrt(2)/4))
Expand expression [src]
         -1          
---------------------
   /     ___________\
   |    /       ___ |
   |   /  1   \/ 2  |
sin|  /   - - ----- |
   \\/    2     4   /
$$- \frac{1}{\sin{\left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \right)}}$$
-1/sin(sqrt(1/2 - sqrt(2)/4))
Common denominator [src]
        -1         
-------------------
   /   ___________\
   |  /       ___ |
   |\/  2 - \/ 2  |
sin|--------------|
   \      2       /
$$- \frac{1}{\sin{\left(\frac{\sqrt{2 - \sqrt{2}}}{2} \right)}}$$
-1/sin(sqrt(2 - sqrt(2))/2)