Given that `(1+sqrt(1+x))tany=1+sqrt(1-x)` . Then `sin4y` is equal to (a)`4x` (b) `2x` (c) `x` (d) none of these

Explanation

To solve the equation \( (1 + \sqrt{1+x}) \tan y = 1 + \sqrt{1-x} \) and find the value of \( \sin 4y \), we can follow these steps:

### Step 1: Substitute \( x \) with \( \cos \theta \)
Let \( x = \cos \theta \). Then we can express \( 1 + x \) and \( 1 - x \) in terms of \( \theta \):
\[ 1 + x = 1 + \cos \theta \]
\[
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