If $$\sqrt{\frac{[(1+CosA)}{2}}=x$$, then find the value of x.

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

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

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

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

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

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

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

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

=> Ans - (D)