1.7 Trigonometry

Prove the identities:

a.

$sec⁡2x−cosec2x≡tan⁡2x−cot⁡2x\sec^2x - \text{cosec}^2x \equiv \tan^2x - \cot^2x$

[2]

b.

$(sec⁡x−cos⁡x)2≡tan⁡2x−sin⁡2x(\sec x - \cos x)^2 \equiv \tan^2x - \sin^2x$

[4]

Prove the identities:

a.

$sec⁡2x−cosec2x≡tan⁡2x−cot⁡2x\sec^2x - \text{cosec}^2x \equiv \tan^2x - \cot^2x$

[2]

b.

$(sec⁡x−cos⁡x)2≡tan⁡2x−sin⁡2x(\sec x - \cos x)^2 \equiv \tan^2x - \sin^2x$

[4]

1.7 Trigonometry Questions