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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