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)(ii) $ \theta = \frac{\pi}{3}$ or $ \theta = \frac{5\pi}{6} $ (b) $ \frac{3}{11} $

2024 CGSS P2 Q3

2024 CGSS P2 Q3