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若cos(a+π/6)=1/4,则sinasin(a+π/3)=
题目详情
若cos(a+π/6)=1/4,则sinasin(a+π/3)=_____
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答案和解析
cos(a+π/6)=cosacosπ/6-sin a sinπ/6=(√3/2)cosa-1/2sina=1/4[(√3/2)cosa-1/2sina]^2=1/4+1/2cos^2a-(√3/2)sinacosa=1/161/2sin^2a=1/2-[-3/16+(√3/2)sinacosa]=11/16-(√3/2)sinacosasinasin(a+π/3)=sinasi...
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