= (csc^2(x) - cot(x) - 2cos^2(x))/1 - cot^2(x)

Post your question with the appropriate groupings making use of brackets please and avoid omitting signs. The way you gave us is this way:




Which is not true.

Sorry I wrote the question wrong this is the correct one, verify this identity: (sin^3(x) cos^3(x)) /(sin(x) + cos(x)) = (csc^2(x) - cot(x) - 2cos^2(x)) / (1 - cot^2(x))

Sorry I wrote this question wrong again this is really the correct one, verify this identity: (sin^3(x) - cos^3(x)) / (sin(x) + cos(x)) = (csc^2(x) - cot(x) - 2cos^2(x)) / (1 - cot^2(x))

Okay.



I think it would be easier to start with the left part:



1. Factorise in the form .
2. Multiply by (sin(x) - cos(x)) in both numerator and denominator.
3. Expand and simplify numerator and denominator.
4. Simplify with identity cos^2(x) + sin^2(x) = 1
5. Expand numerator.
6. Divide numerator and denominator by sin^2(x)