Show that: `int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot`

Explanation

To prove that

\[ \int_0^{\frac{\pi}{2}} f(\sin 2x) \sin x \, dx = \sqrt{2} \int_0^{\frac{\pi}{4}} f(\cos 2x) \cos x \, dx, \]

we will follow these steps:

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