化简:sin²α+sin²(α+π/3)+sin²(α-π/3)

问题描述:

化简:sin²α+sin²(α+π/3)+sin²(α-π/3)

原式=sin²a+(sinacosπ/3+cosasinπ/3)²+(sinacosπ/3-cosasinπ/3)²=sin²a+2sin²acos²π/3+2cos²asin²π/3=sin²a+1/2sin²a+3/2cos²a=3/2(sin²a+cos...