1.7.22 Proofs involving trigonometric functions (A-level only)

Prove the following trigonometric identities:

a.

$cosec2θ−sec⁡2θ≡cot⁡2θ−tan⁡2θ\text{cosec}^2\theta - \sec^2\theta \equiv \cot^2\theta - \tan^2\theta$

[2]

b.

$(cosecθ−sin⁡θ)2≡cot⁡2θ−cos⁡2θ(\text{cosec}\theta - \sin\theta)^2 \equiv \cot^2\theta - \cos^2\theta$

[3]

Prove the following trigonometric identities:

a.

$cosec2θ−sec⁡2θ≡cot⁡2θ−tan⁡2θ\text{cosec}^2\theta - \sec^2\theta \equiv \cot^2\theta - \tan^2\theta$

[2]

b.

$(cosecθ−sin⁡θ)2≡cot⁡2θ−cos⁡2θ(\text{cosec}\theta - \sin\theta)^2 \equiv \cot^2\theta - \cos^2\theta$

[3]

1.7.22 Proofs involving trigonometric functions (A-level only) Questions