Prove the identity $\sin 2x(a \cot x + b \tan x) = a + b + (a - b) \cos 2x$, where $a$ and

Question

Prove the identity $\sin 2x(a \cot x + b \tan x) = a + b + (a - b) \cos 2x$, where $a$ and $b$ are constants.[4] Hence solve the equation $\sin \frac{1}{2}\theta \left( 3 \cot \frac{1}{4}\theta + 5 \tan \frac{1}{4}\theta \right) = 7$ for $0 \le \theta \le 4\pi$.[3]

Accepted Answer

(a) $\sin2x(a\cot x+b\tan x)=a+b+(a-b)\cos2x$, where $\sin x\cos x\ne0$. (b) $\theta=\frac{2\pi}{3}$ or $\frac{10\pi}{3}$.

(A Math) 2025 CCHY PRELIMS P2 Q5

(A Math) 2025 CCHY PRELIMS P2 Q5

Solution:

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