If f : R → R be a continuous function satisfying

Question

If f : \(\mathbb{R}\) → \(\mathbb{R}\) be a continuous function satisfying \(\int\limits_0^{\pi/2}\) f(sin2x). sin x dx + α \(\int\limits_0^{\pi/4}\) f(cos 2x). cos x dx = 0 then α is equal to 

(1) -√3 

(2) √2 

(3) √3 

(4) -√2

Answer 1

Correct option is (4) -√2

Apply king in first part and put x - π/4 = t in second part.