Note: π is spelled "pi", not "pie" like you eat. LOL
  


Two well known identities are


and


Squaring both 


and


Substituting 


and


Substituting 


and


reciprocating both:



and


Answer = -1

Edwin

We have  } = .


THEREFORE,   -  =  -  = .


The numerator is  , by Pythagoras.  THEREFORE, the last fraction in the previous line is -1.


ANSWER.  The expression   -   is identically equal to -1 

         for all values of x different from 0, +/-, +/-, . . . 

         In particular,   -   is -1.

1/tan^2pie/8 - 1/sin^2pie/8

Evaluate

Thanks 

1/tan^2piepi/8 - 1/sin^2piepi/8

       and       
 then becomes: 

IDENTITY: 
              Therefore, 


                              ----- Substituting for