30°+α∈(90°,180°)
sin(30°+α)=4/5
cos(30°+α)=-3/5
1/2 * cosα+√3/2 * sinα=4/5
√3/2 * cosα-1/2 * sinα=-3/5
cosα=(4/5*1/2+ -3/5*√3/2) / (1/4+3/4)
=(4-3√3)/10