a为锐角,sin(a+15°)=4/5,则cos(2a-15°)

a为锐角,sin(a+15°)=4/5,则cos(2a-15°)

sin(a+15°)=4/5,
那么
cos(2a+30°)=1 - 2sin²(a+15°)= -7/25
那么sin(2a+30°)=24/25
所以
cos(2a-15°)
=cos(2a+30°-45°)
=cos(2a+30°)*cos45° +sin(2a+30°)*sin45°
=√2/2 *(24-7)/25
= (17√2)/50