求值cos^2a+cos^2(a+120°)+cos^2(a+240°)
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求值cos^2a+cos^2(a+120°)+cos^2(a+240°)
求值cos^2a+cos^2(a+120°)+cos^2(a+240°)
求值cos^2a+cos^2(a+120°)+cos^2(a+240°)
cos^2a+cos^2(a+120°)+cos^2(a+240°)
=(cosa)^2+{-cos[180-(a+120)]}^2+{-cos[180-(a+240)]}^2
=(cosa)^2+[cos(60-a)]^2+[cos(60+a)]^2
=(cosa)^2+(cos60cosa+sin60sina)^2+(cos60cosa-sin60sina)^2
=(cosa)^2+(1/2*cosa+√3/2*sina)^2+(1/2*cosa-√3/2*sina)^2
=(cosa)^2+1/4(cosa)^2+√3/2sinacosa+3/4(sina)^2+1/4(cosa)^2-√3/2sinacosa+3/4(sina)^2
=3/2*(cosa)^2+3/2*(sina)^2
=3/2*[(sina)^2+(cosa)^2]
=3/2
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