If $f:R\to R$ be a continuous function satisfying ${\int }_{0}^{\pi /2}f(\sin 2x)\cdot \sin xdx+\alpha {\int }_{0}^{\pi /4}f(\cos 2x)\cdot \cos xdx=0$, then $\alpha$ is equal to

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If \(f:R\to R\) be a continuous function satisfying \({\int }_{0}^{\pi /2}f(\sin 2x)\cdot \sin xdx+\alpha {\int }_{0}^{\…

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