Question

请问:2sin60°=sinx+sin(120°-x)

Answer 1

答案:X＝n*π+60° (n为整数,π=180°)
根据2sin60°=sin X +sin(120°- X)
∴ 2sin60°=sin X +sin120°cos X -cos120°sin X
∴ 2*(√3/2)=sin X +(sin120°cos X -cos120°sin X)
∴ 2*(√3)/2)=sin X +( √3)/2)*cos X +(1/2)*sin X
∴ √3=(3/2)*sin X +(√3)/2)*cos X
等式两边同除以 3^(1/2)得
1=(√3)/2)*sin X +(1/2)*cos X
∴ 1=sin(30°+ X)
∵ 1=sin(n*π+90°) (n为整数,π=180°)
∴ 30°+ X=n*π+90° (n为整数,π=180°)
∴ X＝n*π+60° (n为整数,π=180°)