Question

已知a,b均为锐角,且cosa=4/5,cos(a+b)=5/13,则sinb=_____

Answer 1

cosa=4/5,cos(a+b)=5/13

可算得sina=3/5,sin(a+b)=12/13

sinb=sin((a+b)-a)

=sin(a+b)cosa-sinacos(a+b)

=12/13*4/5-5/13*3/5=33/65