Prove the identity $\ \operatorname{cosec} 4x + \cot 4x = \cot 2x$.[3] Hence, find, for \(-18

Question

Prove the identity $\ \operatorname{cosec} 4x + \cot 4x = \cot 2x$.[3] Hence, find, for $-180^\circ \le \theta \le 180^\circ$, the values of $\theta$ for which $\ \operatorname{cosec} 2\theta + \cot 2\theta = -\sqrt{3}$.[4]

Accepted Answer

(a) $\operatorname{cosec}4x+\cot4x=\cot2x$ (proven) (b) $\theta=-30^\circ$ or $150^\circ$

2024 GESS PRELIMS P2 Q7

2024 GESS PRELIMS P2 Q7

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