cos(a+b)=-5/13sinb=3/5,a,b为锐角求cos(a+2b)求sina

Question

cos(a+b)=-5/13 sinb=3/5,a,b为锐角
求cos(a+2b)
求sin a

Answer 1

a,b为锐角
cos(a+b)=-5/13
sin(a+b)=12/13
sinb=3/5,cosb=4/5
cos(a+2b)=cos[(a+b)+b]
=cos(a+b)cosb-sin(a+b)sinb
=-5/13*4/5-12/13*3/5
=-56/65
sin a=sin[(a+b)-b]
=sin(a+b)cosb-cos(a+b)sinb
=12/23*4/5+5/13 *3/5
=63/65