1.7.22 Proofs involving trigonometric functions (A-level only)

Establish the following trigonometric results:

a.

$cosec2ϕ−tan⁡2ϕ≡cot⁡2ϕ−sec⁡2ϕ+2\text{cosec}^2 \phi - \tan^2 \phi \equiv \cot^2 \phi - \sec^2 \phi + 2$

[2]

b.

$(sec⁡x+cos⁡x)2≡tan⁡2x+cos⁡2x+3(\sec x + \cos x)^2 \equiv \tan^2 x + \cos^2 x + 3$

[3]

Establish the following trigonometric results:

a.

$cosec2ϕ−tan⁡2ϕ≡cot⁡2ϕ−sec⁡2ϕ+2\text{cosec}^2 \phi - \tan^2 \phi \equiv \cot^2 \phi - \sec^2 \phi + 2$

[2]

b.

$(sec⁡x+cos⁡x)2≡tan⁡2x+cos⁡2x+3(\sec x + \cos x)^2 \equiv \tan^2 x + \cos^2 x + 3$

[3]

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