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
$\int\left(\frac{\cos 2 x-1}{\cos 2 x+1}\right) d x$
$=\int\left(\frac{1-2 \sin ^2 x-1}{2 \cos ^2 x-1+1}\right) d x$
$=-\int \tan ^2 x d x$
$=-\int\left(\sec ^2 x-1\right) d x$
$=\int\left(1-\sec ^2 x\right) d x$
$=x-\tan x+C$

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