`int(cos2x-1)/(cos2x+1)\ dx=` `tanx-x+C` (b) `x+tanx+C` (c) `x-tanx+C` (d) ` x-cotx+C`

Explanation

To solve the integral \(\int \frac{\cos 2x - 1}{\cos 2x + 1} \, dx\), we will follow these steps:

### Step 1: Simplify the integrand
We start with the expression:
\[ \frac{\cos 2x - 1}{\cos 2x + 1} \]
Using the trigonometric identity \(\cos 2x = 2\cos^2 x - 1\), we can rewrite the integrand:
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