化简函数f(x)=sin(x/2)-√3sin(3π/2+x/2)+α,x∈R ^.^

题目

化简函数f(x)=sin(x/2)-√3sin(3π/2+x/2)+α,x∈R ^.^

答案

f(x)=sin(x/2)-√3sin(3π/2+x/2)+α,
=sin(x/2)+√3cos(x/2)+α
=2[sin(x/2)cosπ/3+cos(x/2)sinπ/3]+α,
=2sin(π/3+x/2)+α