Question

Csc² 0 - cot²0 - sin² 0 = cos² 0

Answer 1

see below

Explanation:

You want to show that csc²(θ) -cot²(θ) -sin²(θ) = cos²(θ).

Proof

It often works well to express the trig functions in terms of sine and cosine. The identity sin²(θ) +cos²(θ) = 1 is also useful.

`\csc^2\theta-\cot^2\theta-\sin^2\theta=\cos^2\theta\\\\(1)/(\sin^2\theta)-(\cos^2\theta)/(\sin^2\theta)-\sin^2\theta=\cos^2\theta\\\\\\(1-\cos^2\theta)/(\sin^2\theta)-\sin^2\theta=\cos^2\theta\\\\\\(\sin^2\theta)/(\sin^2\theta)-\sin^2\theta=\cos^2\theta\\\\\\1-\sin^2\theta=\cos^2\theta\\\\\cos^2\theta=\cos^2\theta\qquad\text{Q.E.D.}`

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