1. ## Limit.

If $A= \lim_{x \to \frac{\pi}{2}}\frac{1-sin^{\lambda+\mu}x}{\sqrt{(1-sin^\lambda x).(1-sin^\mu}x)}$

where $\lambda,\mu>0,$ Then find $A=$

2. Originally Posted by jacks
If $A= \lim_{x \to \frac{\pi}{2}}\frac{1-sin^{\lambda+\mu}x}{\sqrt{(1-sin^\lambda x).(1-sin^\mu}x)}$

where $\lambda,\mu>0,$ Then find $A=$
You can use L'Hopitals Rule. Have you tried that?

3. but Using L.Hospital this is very Complicated.....

4. The solution is $\displaystyle\frac{\lambda+\mu}{\sqrt{\lambda\mu}}$

The only way I see you bringing the lambda and mu down is by applying the rule.