Question
If $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function satisfying $\int_\limits{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_\limits{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0$, then the value of $\alpha$ is :
If $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function satisfying $\int_\limits{0}^{\frac{\pi}{2}} f(\sin 2 x) \sin x d x+\alpha \int_\limits{0}^{\frac{\pi}{4}} f(\cos 2 x) \cos x d x=0$, then the value of $\alpha$ is :