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Question

Prove that sin2x+ sin2(x+π/3)+sin2(x-π/3)=3/2

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Solution

sin^2x + (sinx cospi/3 + cosx sinpi/3)^2 + (sinx cos pi/3 - cosx sinpi/3)^2
sin^2 x + (2sin^2x cos^2 pi/x) + (2cos^x sin^ pi/3)
sin^2 x + 1/2 sin^x + 3/2(1-sin^2 x)
3/2 sin^2 x + 3/2 - 3/2 sin^ x
3/2 = Answer
hence proved

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