Prove $\operatorname{cosec} 2\theta - \cot 2\theta = \tan\theta$.[3] Hence, solve \(\operatorname{

Question

Prove $\operatorname{cosec} 2\theta - \cot 2\theta = \tan\theta$.[3] Hence, solve $\operatorname{cosec} 4\theta - \cot 4\theta = -\sqrt{3}$ for $0 < \theta < \pi$.[2] The angles $A$ and $B$ are such that[5] $\sin(A + 45^{\circ}) = (2\sqrt{2})\cos A$ and $4\sec^2 B + 5 = 12\tan B$. Without using a calculator, find the exact value of $\tan(A - B)$.

Accepted Answer

(a)(i) $\operatorname{cosec}2\theta-\cot2\theta=\tan\theta$, where defined. (a)(ii) $\theta=\frac\pi3,\frac{5\pi}6$. (b) $\tan(A-B)=\frac3{11}$.

2024 CGSS P2 Q3

2024 CGSS P2 Q3

Solution:

Solution locked