Question

Please simplify, 50 points.

(sin Θ - cos Θ) - (sin Θ + cos Θ)^2

Answer 1

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)

Explanation: