Somemathhere

Evaluate $$\int_{0}^{\pi/2}(\tan x)^a\text{d}x$$ $$\int_{0}^{\pi/2}\int_{0}^{\pi/2}\left(\frac{\sin x}{\sin y}\right)^a\text{d}x\text{d}y$$ (in particular for $a=1/2$, the answes is $\pi$.) Solution. Use the Beta function trigonometric definition.