$\int \dfrac{1-\sin x}{\cos^2 x}\,dx$ equals

Question

Accepted Answer

C. $	an x-\sec x+C$

1. Split: $\dfrac{1}{\cos^2 x}-\dfrac{\sin x}{\cos^2 x}=\sec^2 x-	an x\sec x$.
2. $\int \sec^2 x\,dx=	an x$.
3. $\int \sec x	an x\,dx=\sec x$, subtracted gives $-\sec x$.
4. Result: $	an x-\sec x+C$. Option A wrongly adds $\sec x$.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.295_

Answer

$	an x+\sec x+C$

Answer

$\sec x-	an x+C$

Answer

$\cot x-\operatorname{cosec} x+C$