2sinα-cosα=根号3sinα,则cosα

2sinα-cosα=根号3sinα,则cosα

2sinα-cosα=根号3sinα
cosα = (2-根号3)sinα
cos^2α=(2-根号3)^2 sin^2α=(7-4根号3) (1-cos^2α)
(1+7-4根号3)cos^2α=7-4根号3
4(2-根号3)cos^2α=(2-根号3)^2
cos^2α=1/2-根号3/4 = {(根号6-根号2)/4}^2
cosα = ± (根号6-根号2) /4