Prove $\dfrac{\cos 2\theta}{\tan \theta}+\sin 2\theta=\cot \theta$.[4] Solve \(3\sin x\tan x-\sec

Question

Prove $\dfrac{\cos 2\theta}{\tan \theta}+\sin 2\theta=\cot \theta$.[4] Solve $3\sin x\tan x-\sec x=1$ for $-180^\circ\leq x\leq 180^\circ$.[6]

Accepted Answer

(a) $\dfrac{\cos 2\theta}{\tan\theta}+\sin 2\theta=\cot\theta$ (b) $x=-180^\circ,-48.2^\circ,48.2^\circ,180^\circ$

2025 TKSS PRELIMS P2 Q11