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cos? o+ cos? (a+120) + cos? ( â120") = |
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Answer» cos 120 = cos (90 +30) = cos90cos30 - sin90sin30 = -1/2sin 120 = cos90sin30+ sin90cos30 = sqrt3/2cos²( α + 120° ) =(-1/2*cosα -sqrt3/2*sinα)^2 = 1/4*(cosα + sqrt3*sinα)^2cos² ( α - 120° ) =(-1/2*cosα + sqrt3/2*sinα)^2 = 1/4*(cosα - sqrt3*sinα)^2 therefore given identity is= cos² α + 1/4*cos² α + 1/4*cos² α +3/4*(1-cos² α) + 3/4*(1-cos² α)= 3/2. |
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