Q. 7

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

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


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