Question

已知a,b为锐角,且cosa=3/5,sin(a-b)=5/13,求cosb的值

Answer 1

∵a,b为锐角,cosa=3/5,sin(a-b)=5/13

∴sina=4/5,cos(a-b)=12/13

∴cosb=cos[(b-a)+a]=cos(b-a)cosa-sin(b-a)sina]=cos(a-b)cosa+sin(a-b)sina=(12/13)*(3/5)+(5/13)*(4/5)=56/65