Question

Differentiate $\frac{\cos 2x}{{\sin }^{2}x\cdot {\cos }^{2}x}$

Answer 1

$\frac{d}{dx}\left(\frac{cos2x}{si{n}^{2}xco{s}^{2}x}\right)=\frac{d}{d_x}\left(\frac{4cos2x}{4si{n}^{2}xco{s}^{2}x}\right)$

$=\frac{d}{dx}\left(\frac{4cos2x}{si{n}^{2}2x}\right)$

$=\frac{si{n}^{2}2x.(-8sin2x)-4cos2x.2sin2x.2cos2x}{si{n}^{4}2x}$

$=\frac{-8si{n}^{3}2x-16sin2x.co{s}^{2}2x}{si{n}^{4}2x}$

$=-8cosec2x-16co{t}^{2}2x.cosec2x$

$=-8cosec2x(1+2co{t}^{2}2x)$