Limit.

[man111]

Calculate $\lim_{x \to \frac{\pi}{2}}\frac{1-sin^{\lambda+\mu}x}{\sqrt{(1-sin^\lambda x).(1-sin^\mu}x)}$
where $\lambda,\mu>0$.

[ewert]

$\dfrac{\lambda+\mu}{\sqrt{\lambda\mu}}$

[man111]

can you explain it.....

[gris]

$\sin (\pi/2-x)=\cos x$
$\cos x\sim ...$
$(1-x)^a\sim...$

[man111]

Thanks gris I have got it.

(I have done using L. Hospital) very Lengthy....