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sina=1/3则sin3a=?
题目详情
sin a=1/3 则sin 3a=?
▼优质解答
答案和解析
sin(3a)=sin(2a+a)
=sin(2a)cosa+cos(2a)sina
=2sinacosacosa+[1-2(sina)^2]sina
=2sina[1-(sina)^2]+sina-2(sina)^3
=2sina-2(sina)^3+sina-2(sina)^3
=3sina-4(sina)^3
=3(1/3)-4(1/3)^3
=1-4/27
=23/27
=sin(2a)cosa+cos(2a)sina
=2sinacosacosa+[1-2(sina)^2]sina
=2sina[1-(sina)^2]+sina-2(sina)^3
=2sina-2(sina)^3+sina-2(sina)^3
=3sina-4(sina)^3
=3(1/3)-4(1/3)^3
=1-4/27
=23/27
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