p=cos^2α+cos^2(60度-α)+cos^2(60度+α)的值?

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p=cos^2α+cos^2(60度-α)+cos^2(60度+α)的值?
p=cos^2α+cos^2(60度-α)+cos^2(60度+α)的值?

p=cos^2α+cos^2(60度-α)+cos^2(60度+α)的值?
p=cos²a+(cosacos60+sin60sina)²+(cosacos60-sin60sina)²
=cos²a+cos²acos²60+2cosacos60sin60sina+sin²60sin²a+cos²acos²60-2cosacos60sin60sina+sin²60sin²a
=cos²a+2cos²acos²60+2sin²60sin²a
=cos²a+2cos²a*1/4+2*3/4sin²a
=cos²a+2cos²a*1/4+2*3/4sin²a
=3/2*cos²a+3/2*sin²a
=3/2*(cos²a+sin²a)
=3/2