Some integrals

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.

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