a为锐角,若cos(a+派/2)=4/5,则sin(2a+派/12)的值为?
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![a为锐角,若cos(a+派/2)=4/5,则sin(2a+派/12)的值为?](/uploads/image/z/3854485-37-5.jpg?t=a%E4%B8%BA%E9%94%90%E8%A7%92%2C%E8%8B%A5cos%EF%BC%88a%2B%E6%B4%BE%2F2%EF%BC%89%EF%BC%9D4%EF%BC%8F5%2C%E5%88%99sin%EF%BC%882a%2B%E6%B4%BE%EF%BC%8F12%EF%BC%89%E7%9A%84%E5%80%BC%E4%B8%BA%3F)
a为锐角,若cos(a+派/2)=4/5,则sin(2a+派/12)的值为?
a为锐角,若cos(a+派/2)=4/5,则sin(2a+派/12)的值为?
a为锐角,若cos(a+派/2)=4/5,则sin(2a+派/12)的值为?
题目有错吧.a为锐角时,cos(a+派/2)的值必须是负数.如果是-4/5的话,
cos(a+派/2)=-4/5推出sina=4/5,则sosa=3/5
sin(2a+派/12)=sin2a*cos派/12+cos2a*sin派/12
=2sina*cosa*(根号6+根号2)/4+(1-2*sin^2 a)*(根号6-根号2)/4
=2*4/5*3/5*(根号6+根号2)/4+(1-2*16/25)*(根号6-根号2)/4
=(21根号6+3根号2)/50