若α是锐角,且满足sin(α-π/6)=1/3,求cosα的值
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若α是锐角,且满足sin(α-π/6)=1/3,求cosα的值
若α是锐角,且满足sin(α-π/6)=1/3,求cosα的值
若α是锐角,且满足sin(α-π/6)=1/3,求cosα的值
sin(a -π/6 )=1/3,
sinacosπ/6-cosasinπ/6=1/3
√3sina/2-cosa/2=1/3
√3sina-cosa=2/3
√3sina=coaa+2/3
两边平方
3(sina)^2=(cosa)^2+4cosa/3+4/9
3-3(cosa)^2=(cosa)^2+4cosa/3+4/9
令x=cosa
4x^2+4x/3-23/9=0
36x^2+12x-23=0
x=(-1±2√6)/6
因为α为锐角
所以0
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