Write the values of x in [0, π] for which and cos 2x are in A.P.

Question

Philoid · Accepted Answer

a, a+r, a+2r

so A₁+A₃=2A₂

here sin2x + cos2x = 1

2sin x cos x + 1-2sin²x =1

sin x cos x - sin²x=0

sin x (cos x-sin x)=0

if sin x =0

then x =0, π

if sin x=cos x

then x = π/4

So, all possible values are