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If f:\mathbbR\to\mathbbR is a continuous function satisfying \[ ∫_0^π/2 f(\sin 2x)\,\sin x\,dx \;+\; α ∫_0^π/4 f(\cos 2x)\,\cos x\,dx \;=\; 0, \] then the value of α is: | Watch the step-by-step video solution for this NIMCET PYQ.