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化简sin^2（α-π/6）+sin^2（α+π/6）-sin^2α=?
题目详情
化简 sin^2（α-π/6）+sin^2（α+π/6）-sin^2α=________________?
▼优质解答
答案和解析
答案为：1/2.
sin²（α-π/6）+sin²（α+π/6）-sin²α
=[1-cos(2α-π/3)]/2+[1-cos(2α+π/3)]/2-（1-cos2α）/2
=1/2 +（1/2）cos2α-（1/2）*[cos(2α-π/3)+cos(2α+π/3)]
=1/2 +(1/2)cos2α-(1/2)cos2α
=1/2.
sin²（α-π/6）+sin²（α+π/6）-sin²α
=[1-cos(2α-π/3)]/2+[1-cos(2α+π/3)]/2-（1-cos2α）/2
=1/2 +（1/2）cos2α-（1/2）*[cos(2α-π/3)+cos(2α+π/3)]
=1/2 +(1/2)cos2α-(1/2)cos2α
=1/2.
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