Mathematics

Problem

Let

\alpha, \beta

be two distinct values of

x

lying in

[0, \pi]

for which

\sqrt{5} \sin x, 10 \sin x, 10(4 \sin^2 x + 1)

are 3 consecutive terms of a G.P. Then minimum value of

|\alpha - \beta| =

(a)

\frac{\pi}{10}

(b)

\frac{\pi}{5}

(c)

\frac{2\pi}{5}

(d)

\frac{3\pi}{5}