证明2sin(60°+α)cos(60°-α)=√3/2+sin2α,麻烦写下具体步骤.
题目
证明2sin(60°+α)cos(60°-α)=√3/2+sin2α,麻烦写下具体步骤.
答案
左边=sin(60°+α)cos(60°-α)+sin(60°+α)cos(60°-α)
=[sin(60°+α)cos(60°-α)+cos(60°+α)sin(60°-α)]+[sin(60°+α)cos(60°-α)-cos(60°+α)sin(60°-α)]
=sin[(60°+α)+(60°-α)]+sin[(60°+α)-(60°-α)]
=sin120°+sin2α
=√3/2+sin2α
=右边 .
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