Question

Simplify: (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3

Answer 1

The trigonometric equation  (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3 can be simplified by:

Using x for Θ: 

(sinx - cosx)^2 - (sinx + cosx)^2 
= (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x) 
= - 2 sinx cosx - 2 sinx cosx 
= - 4 sinx cosx 
= - 2sin(2x) 

I hope it has come to your help.