Class 11thProve thatcos²A + cos²(A+2π/3) + cos²(A - 2π/3) = 3/2
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cos^2A + cos^2 (A + 2pi/3) +cos^2 (A -2pi/3)=3/2
LHS =cos^2A +{cosA.cos2pi/3-sinA.sin2pi/3}^2 +{cosA.cos2pi/3+sinA.sin2pi/3}^2
=cos^2A + 2cos^2A.cos^2(2pi/3)+2sin^2A.sin^2 (2pi/3)
=cos^2A +cos^2A /2 + 3/2sin^2A
=3/2 {sin^2A + cos^2A}
=3/2 =RHS
hence proved
LHS =cos^2A +{cosA.cos2pi/3-sinA.sin2pi/3}^2 +{cosA.cos2pi/3+sinA.sin2pi/3}^2
=cos^2A + 2cos^2A.cos^2(2pi/3)+2sin^2A.sin^2 (2pi/3)
=cos^2A +cos^2A /2 + 3/2sin^2A
=3/2 {sin^2A + cos^2A}
=3/2 =RHS
hence proved
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