函数y=cos(x+π/2）+sin（π/3-x)化简

题目

函数y=cos(x+π/2）+sin（π/3-x)化简

答案

y=cos(x+π/2）+sin（π/3-x)
y=-sinx+sinπ/3cosx-sinxcosπ/3
=-sinx+√3cosx/2-sinx/2
=√3cosx/2-3sinx/2
=√3(cosx/2-√3sinx/2)
=√3sin(π/6-x)