If `tan(pi/4+y/2)=tan^3(pi/4+x/2)dot` Prove that `(siny)= (sinx)(3+sin^2x)/(1+3sin^2x)` .

Explanation

To prove that \( \sin y = \frac{\sin x (3 + \sin^2 x)}{1 + 3 \sin^2 x} \) given that \( \tan\left(\frac{\pi}{4} + \frac{y}{2}\right) = \tan^3\left(\frac{\pi}{4} + \frac{x}{2}\right) \), we will follow these steps:

### Step 1: Rewrite the given equation using the tangent addition formula
Using the tangent addition formula, we have:
\[ \tan\left(\frac{\pi}{4} + \frac{y}{2}\right) = \frac{1 + \tan\left(\frac{y}{2}\right)}{1 - \tan\left(\frac{y}{2}\right)} \]
Similarly,
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