Question

Please simplify, 50 points.

(sin Θ - cos Θ) - (sin Θ + cos Θ)^2

Answer choices are attached.

Answer 1

D

Explanation:

Expand (sinΘ + cosΘ)²

= sinΘ - cosΘ - (sin²Θ + 2 sinΘcosΘ + cos²Θ)

= sinΘ - cosΘ - sin²Θ - 2sinΘcosΘ - cos²Θ

= sinΘ - cosΘ - 2sinΘcosΘ - (sin²Θ + cos²Θ)

= - 2sinΘcosΘ - cosΘ + sinΘ - 1 → D

Answer 2

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)

Explanation: