Solve the equation, `(1-tanx)(1+sin2x)=1+tanx`

Explanation

To solve the equation \( (1 - \tan x)(1 + \sin 2x) = 1 + \tan x \), we will follow these steps:

### Step 1: Substitute the formula for \(\sin 2x\)
We know that:
\[ \sin 2x = \frac{2 \tan x}{1 + \tan^2 x} \]
Substituting this into the equation gives:
...