\(\int\frac{d\mathrm x}{\sin^2\mathrm x\cos^2\mathrm x}\) \(=\int \frac{\sin^2\mathrm x+\cos^2\mathrm x}{\sin^2\mathrm x\cos^2\mathrm x}d\mathrm x\) (\(\because\) sin2x + cos2x = 1)
\(=\int \frac{1}{\cos^2\mathrm x}d\mathrm x\) + \(\int \frac{1}{\sin^2\mathrm x}d\mathrm x\)
\(=\int \sec^2\mathrm xd\mathrm x\) + \(\int \mathrm{cosec^2xd x}\)
= tan x – cot x + C, where C is an integral constant.
\((\because\) \(\int\)sec2x dx = tan x and \(\int\)cosec2x dx = –cot x)
