Given that $y = \ln \left( \sin^2 x \right)$, show that \(\frac{\mathrm{d}y}{\mathrm{d}x

Question

Given that $y = \ln \left( \sin^2 x \right)$, show that $\frac{\mathrm{d}y}{\mathrm{d}x} = 2 \cot x$.[2] Hence, show that the value of $\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (\cot x - \cos^2 2x) \, \mathrm{d}x = a + b \ln 2$, where $a$ and $b$ are constants.[4]

Accepted Answer

(b)a=$-\frac{\pi}{8}$, b =$\frac{1}{2}$

2025 AHS PRELIMS P1 Q12

2025 AHS PRELIMS P1 Q12