Question

How do you verify this trigonometric identity? cos^2 θcot^2 θ = cot^2 θ - cos^2 θ

Answer 1

Explanation:

Replace cos^2(θ) with 1-sin^2(θ), and cot(θ) with cos(θ)/sin(θ).

cos^2(θ)cot^2(θ) = cot^2(θ) - cos^2(θ)

(1 -sin^2(θ))cot^2(θ) = . . . . . replace cos^2 with 1-sin^2

cot^2(θ) -sin^2(θ)·cos^2(θ)/sin^2(θ) = . . . . . replace cot with cos/sin

cot^2(θ) -cos^2(θ) = cot^2(θ) -cos^2(θ) . . . as desired