a是锐角,且sin(a-π/6)=1/3,则cosa为

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a是锐角,且sin(a-π/6)=1/3,则cosa为
a是锐角,且sin(a-π/6)=1/3,则cosa为

a是锐角,且sin(a-π/6)=1/3,则cosa为
√3/2*sina-0.5cosa=1/3
27(1-cos^2a)=4+9cos^2a+12cosa
36cos^2a+12cosa-23=0
cosa=-1/6±[√12^2+4*6^2*23]/72
=-1/6±√6/6

sin(a-π/6)=1/3
sinacosπ/6-sinπ/6cosa=1/3
√3/2sina-cosa/2=1/3
√3sina-cosa=2/3
又sin²a+cos²a=1
∴sin²a+(√3sina-2/3)²=1
∴sina=(√3+2√2)/6

a是锐角,00
且sin(a-π/6)=1/3,则:cos(a-π/6)=2√2/3
cosa=cos[(a-π/6)+π/6]
=cos(a-π/6)cosπ/6-sin(a-π/6)sinπ/6
= 2√2/3 * √3/2 - 1/3 *1/2
=(2√6-1)/6