Question

prove that cos@/1-tan@ - sin^2 @/cos@-sin@=sin@+cos@

Answer 1

We want to prove that

cosa1−tana+sina1−cota=cosa+sina

Rewrite the left using only sines and cosines:

cosa1−sinacosa+sina1−cosasina=cos2acosa−sina+sin2asina−cosa

Pulling a −1 out of the denominator of the second term gives us the same denominator:

=cos2acosa−sina−sin2acosa−sina=cos2a−sin2acosa−sina

Factoring:

=(cosa+sina)(cosa−sina)cosa−sina=cosa+sina

Which was originally the right hand side, so this is proven.