3.4 Trigonometry (A-level only)

Prove the following identities for all valid values of $A$ :

a.

$sec⁡2A+cosec2A≡tan⁡2A+cot⁡2A+2\sec^2 A + \text{cosec}^2 A \equiv \tan^2 A + \cot^2 A + 2$

[2]

b.

$(tan⁡A+cot⁡A)2≡sec⁡2A+cosec2A(\tan A + \cot A)^2 \equiv \sec^2 A + \text{cosec}^2 A$

[3]

Prove the following identities for all valid values of $A$ :

a.

$sec⁡2A+cosec2A≡tan⁡2A+cot⁡2A+2\sec^2 A + \text{cosec}^2 A \equiv \tan^2 A + \cot^2 A + 2$

[2]

b.

$(tan⁡A+cot⁡A)2≡sec⁡2A+cosec2A(\tan A + \cot A)^2 \equiv \sec^2 A + \text{cosec}^2 A$

[3]

3.4 Trigonometry (A-level only) Questions