A.Maths

if θ is an acute angle and the equation in x (3cosθ)x^2-(4sinθ)x+2=0 has equal roots,find θ
Equal roots means that the discriminant (D=b^2-4ac) equals to 0
So
[-(4sinθ)]^2-4(3cosθ)(2)=0
16sin^2θ-24cosθ=0
2sin^2θ-3cosθ=0
2(1-cos^2θ)-3cosθ=0
2cos^2θ+3cosθ-2=0
(2cosθ-1)(cosθ+2)=0
cosθ=1/2 or cosθ=-2 (rejected because -1<=cosθ<=1)
So θ=π/3