y=﹙sinx)的平方+[sin(x+π/3)]的平方+[sin(x-π/3)]的平方
sin(x﹢π/3)=sinxcosπ/3﹢cosxsinπ/3=sinx／2﹢√3cosx／2
sin(x﹣π/3)=sinxcosπ/3﹣cosxsinπ/3=sinx／2﹣√3cosx／2
[sin(x+π/3)]的平方=﹙sinx／2﹢√3cosx／2﹚²=﹙sin²x﹢3cos²x+2√3sinxsosx﹚／4
[sin(x-π/3)]的平方=﹙sinx／2﹣√3cosx／2﹚²=﹙sin²x﹢3cos²x﹣2√3sinxsosx﹚／4
∴y=﹙sinx)的平方+[sin(x+π/3)]的平方+[sin(x-π/3)]的平方
=sin²x+﹙sin²x﹢3cos²x﹚／2
=3﹙sin²x﹢cos²x﹚／2
=3/2
∴y的最大值=3/2