If sin(A/2) = x, then the value of x is

Using double angle formula, we know that $$cos(2\theta) = cos^2\theta - sin^2\theta$$

=> $$cos(2\theta) = (1 - sin^2\theta) - sin^2\theta$$

=> $$cos(2\theta) = 1 - 2sin^2\theta$$

Replacing $$\theta$$ by $$\frac{A}{2}$$, we get :

=> $$cos A = 1 - 2sin^2(\frac{A}{2})$$

=> $$2sin^2(\frac{A}{2}) = 1 - cosA$$

=> $$sin^2(\frac{A}{2}) = \frac{(1-cosA)}{2}$$

=> $$sin(\frac{A}{2}) = \sqrt{\frac{(1 - cos A)}{2}}$$

=> Ans - (B)