Question

Simplify: (sin θ − cos θ)^2 − (sin θ + cos θ)^2 A) −4sin(θ)cos(θ) B) 2 C) sin^2 θ D) cos^2 θ

Answer 1

-4sinθcosθ

Explanation:

Note:

1. (a + b)^2 = a^2 + 2ab + b^2

2. (a - b)^2 = a^2 - 2ab + b^2

3. sin^2θ + cos^2θ = 1

(sinθ -cosθ)^2 - (sinθ + cosθ)^2

= sin^2θ - 2sinθcosθ + cos^2θ - (sin^2θ + 2sinθcosθ + cos^2θ)

= sin^2θ + cos^2θ - 2sinθcosθ - (sin^2θ + cos^2θ + 2sinθcosθ)

= 1 - 2sinθcosθ - (1 + 2sinθcosθ)

= 1- 2sinθcosθ -1 - 2sinθcosθ

= - 2sinθcosθ - 2sinθcosθ

= -4sinθcosθ