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.
