已知cos(a+40°)=3/5,a为锐角,则sin(2a+20°)=

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已知cos(a+40°)=3/5,a为锐角,则sin(2a+20°)=
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已知cos(a+40°)=3/5,a为锐角,则sin(2a+20°)=
已知cos(a+40°)=3/5,a为锐角,则sin(2a+20°)=

已知cos(a+40°)=3/5,a为锐角,则sin(2a+20°)=
cos(a+40°)=3/5, a为锐角,
∴a+40°是锐角,
sin(a+40°)=4/5,
∴cos(a+10°)=cos(a+40°-30°)=3/5*√3/2+4/5*1/2=(3√3+4)/10,
sin(a+10°)=sin(a+40°-30°)=4/5*√3/2-3/5*1/2=(4√3-3)/10,
∴sin(2a+20°)=2(4√3-3)/10*(3√3+4)/10
=(24+7√3)/50.