Question

The value of $\int \frac{(\cos 2x-1)}{(\cos 2x+1)}dx$ is

• A. $\tan x–x+C$
• B. $\tan x+x+C$
• C. $x–\tan x+C$
• D. $-x–cotx+C$

Answer 1

The correct option is C

$x–\tan x+C$

The explanation for the correct answer.

Evaluate the integral.

$\int \frac{(\cos 2x-1)}{(\cos 2x+1)}dx$

$$\begin{gathered} =–\int \frac{(2{\sin }^{2}x)}{(2{\cos }^{2}x)}dx \\ =–\int {\tan }^{2}xdx \\ =\int (1–se{c}^{2}x)dx \\ =x–\tan x+C \end{gathered}$$

Hence, option C is correct .