证明:(sinx)^2+sin(x+60度)^2+sin(x+120度)^2=3/2
问题描述:
证明:(sinx)^2+sin(x+60度)^2+sin(x+120度)^2=3/2
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答
(sinx)^2+sin(x+60度)^2+sin(x+120度)^2=sin²x+sin²(x+60°)+sin²(x-60°)=sin²x+(1/2sinx+√3/2cosx)²+(1/2sinx-√3/2cosx)²=sin²x+1/2sin²x+3/2cos²x=3/2(sin...