cos^2x+cos^2[x+π/3]+cos^2[x-π/3]=3/2

Prove that
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1 Answer

cos(x+(pi)/3)=(cosx)/2-(sinx)sqrt(3)/2; cos^2(x+(pi)/3)=cos^2x/4-sinxcosxsqrt(3)/2+3sin^2x/4

cos(x-(pi)/3)=(cosx)/2+(sinx)sqrt(3)/2; cos^2(x-(pi)/3)=cos^2x/4+sinxcosxsqrt(3)/2+3sin^2x/4

Add these together: cos^2x/2+3sin^2x/2 and add cos^2x=(3/2)(cos^2x+sin^2x)=3/2 QED.
by Top Rated User (1.2m points)

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