Show that $\sin 2x \cot x = 2 \cos^2 x$.[1] Hence, without using a calculator, find the value

Question

Show that $\sin 2x \cot x = 2 \cos^2 x$.[1] Hence, without using a calculator, find the value of the constant $k$ for which $\int_{\frac{\pi}{18}}^{\frac{\pi}{9}} \operatorname{cosec} 6x \tan 3x \; \mathrm{d}x = \frac{\sqrt{3}}{k}$.[5]

Accepted Answer

(b) $k = 9$

2024 CCHY P1 Q13

2024 CCHY P1 Q13