limits - Evaluate $lim_{xto pi/2} frac{sqrt{1+cos(2x)}}{sqrt{pi}-sqrt{2x}}$

Evaluate
$$\lim_{x\to \pi/2} \frac{\sqrt{1+\cos(2x)}}{\sqrt{\pi}-\sqrt{2x}}$$

I tried to solve this by L'Hospital's rule..but that doesn't give a solution..appreciate if you can give a clue.