Within what limits must `A/2` lie if `2sin(A/2)=sqrt(1+sinA)-sqrt(1-sinA)`

Explanation

To solve the equation \( 2\sin\left(\frac{A}{2}\right) = \sqrt{1 + \sin A} - \sqrt{1 - \sin A} \), we will follow these steps:

### Step 1: Simplify the Right Side
Start by simplifying the right-hand side of the equation. We know that:
\[ \sqrt{1 + \sin A} - \sqrt{1 - \sin A} \]
We can use the identity \( \sin A = 2\sin\left(\frac{A}{2}\right)\cos\left(\frac{A}{2}\right) \) to express \( \sin A \) in terms of \( \sin\left(\frac{A}{2}\right) \) and \( \cos\left(\frac{A}{2}\right) \).
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