x为锐角,sin(x+15°)=4/5,则cos(2x-15°)=?
问题描述：
x为锐角,sin(x+15°)=4/5,则cos(2x-15°)=?
答
2x-15=2(x+15)-45
因为sin(x+15°)=4/5
所以cos(x+15°)=3/5
sin(2x+30°)=2*4/5*3/5=24/25
cos(2x+30°)=-7/25
故cos(2x-15°)=cos（(2x+30°)-45）=cos(2x+30°)cos45+sin(2x+30°)sin45
=-7/25cos45+24/25sin45=17√2/50