$\int \dfrac{dx}{\sin^2 x\cos^2 x}$ equals

1. Write $\dfrac{1}{\sin^2 x\cos^2 x}=\dfrac{\sin^2 x+\cos^2 x}{\sin^2 x\cos^2 x}$. 2. Split into $\dfrac{1}{\cos^2 x}+\dfrac{1}{\sin^2 x}=\sec^2 x+\operatorname{cosec}^2 x$. 3. $\int \sec^2 x\,dx=\tan x$ and $\int \operatorname{cosec}^2 x\,dx=-\cot x$. 4. Sum: $\tan x-\cot x+C$. Option A wrongly adds $\cot x$. _Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.304_