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If f is an even function, then prove that ∫ f(cos 2x)cos x (for x → 0, pi/2) dx = √2 ∫ f(sin 2x)cos x (for x → 0,pi/4) dx

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If f is an even function, then prove that

∫ f(cos 2x)cos x (for x → 0, pi/2) dx = √2 ∫ f(sin 2x)cos x (for x → 0,pi/4) dx

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On adding Eqs. (i) and (ii), we get

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