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## Main Question or Discussion Point

I am trying to follow a proof of [tex]\Gamma(\frac{1}{2}) = \sqrt{\pi}[/tex] but in the way i have found this equality:

[tex]\int_{0}^\frac{\pi}2sin^n xdx = \int_{0}^\frac{\pi}2cos^n xdx[/tex].

I have tried unsucessfully integration for parts and I don't see how can I make some substitution. Maybe you can help me to justify this equation?

(Note.- The fraction in the upper limit has a pi)

Thanks.

[tex]\int_{0}^\frac{\pi}2sin^n xdx = \int_{0}^\frac{\pi}2cos^n xdx[/tex].

I have tried unsucessfully integration for parts and I don't see how can I make some substitution. Maybe you can help me to justify this equation?

(Note.- The fraction in the upper limit has a pi)

Thanks.