Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integration2 Marks
MCQ
$\int \frac{\cos (2 x)-1}{\cos (2 x)+1} d x=$______.
A
tan x-x + c
B
x + tan x + c
C
x- tan x + c
D
- x - cot x + c
✓
Answer
$x-\tan x+c$
$\begin{aligned} \int \frac{\cos 2 x-1}{\cos 2 x+1} d x & =\int \frac{-(1-\cos 2 x)}{(1+\cos 2 x)} d x \\ =-\int \frac{2 \sin ^2 x}{2 \cos ^2 x} d x & =-\int \tan ^2 x d x \\ & =-\int\left(\sec ^2 x-1\right) d x \\ & =-(\tan x-x)+c \\ & =x-\tan x+c\end{aligned}$
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