已知sin(a+π/3）=3/5 a属于（π/6,2π/3） 则cosa=?

题目

已知sin(a+π/3）=3/5 a属于（π/6,2π/3） 则cosa=?

答案

sin(a+π/3)=3/5
a∈(π/6,2π/3)
a+π/3∈(π/2,π)
所以cos(a+π/3)<0
cos(a+π/3)=-4/5
cosa=cos(a+π/3-π/3)
=1/2cos(a+π/3)+√3/2sin(a+π/3)
=(3√3-4)/10