已知2sinγ-cosγ=根号3*sinγ,求cosγ,sinγ的值

已知2sinγ-cosγ=根号3*sinγ,求cosγ,sinγ的值
已知2sinγ-cosγ=根号3*sinγ,求cosγ,sinγ的值

已知2sinγ-cosγ=根号3*sinγ,求cosγ,sinγ的值
(2-√3)sinγ=cosγ
平方
(2-√3)²sin²γ=cos²γ=1-sin²γ
sin²γ=1/(3-√3)=(3+√3)/6
sinγ=±√[(3+√3)/6]
cosγ=(2-√3)sinγ
所以
sinγ=√[(3+√3)/6],cosγ=√[(9-5√3)/6]
或sinγ=-√[(3+√3)/6],cosγ=-√[(9-5√3)/6]

(2-根号3)sinγ=cosγ
(sinγ)^2+(cosγ)^2=1
(sinγ)^2+(7-4根号3)(sinγ)^2=1
(sinγ)^2=1/(8-4根号3)=(2+根号3)/4
sinγ=(根号6+根号2)/4, cosγ=(根号6-根号2)/4
或sinγ=-(根号6+根号2)/4, cosγ=-(根号6-根号2)/4