化简:sin²α+sin²(α+π/3)+sin²(α-π/3)
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化简:sin²α+sin²(α+π/3)+sin²(α-π/3)
![化简:sin²α+sin²(α+π/3)+sin²(α-π/3)](/uploads/image/z/20005608-48-8.jpg?t=%E5%8C%96%E7%AE%80%EF%BC%9Asin%26%23178%3B%CE%B1%2Bsin%26%23178%3B%EF%BC%88%CE%B1%2B%CF%80%2F3%EF%BC%89%2Bsin%26%23178%3B%EF%BC%88%CE%B1-%CF%80%2F3%EF%BC%89)
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+cos²a)
=3/2
=sin²a+2sin²acos²π/3+2cos²asin²π/3
=sin²a+1/2sin²a+3/2cos²a
=3/2(sin²a+cos²a)
=3/2
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