Question

If $I=\int (\sec x-\sin x\tan x)dx,$ then the value of $I$ is
(where $C$ is constant of integration)

• A. $\sin x+C$
• B. $\cos x+C$
• C. $-\cot x+C$
• D. $\tan x+C$

Answer 1

The correct option is A $\sin x+C$

$I=\int (\sec x-\sin x\tan x)dx$
$\Rightarrow I=\int (\frac{1}{\cos x}-\frac{{\sin }^{2}x}{\cos x})$
$\Rightarrow I=\int \frac{{\cos }^{2}x}{\cos x}dx$

$\Rightarrow I=\int \cos xdx=\sin x+C$