Solve the equation 3sin^2(x) + sin(x) + 8 = 9cos^2(x), -180<X<180. Then find smallest positive solution of 3sin^2(2O-30) + sin(2O-30) + 8 = 9cos^2(2O-30).

Cos^2(x) + sin^2(x) = 1. Therefore Cos^2(x) = 1 - sin^2(x). So equation becomes 3Sin^2(x) + sin(x) + 8 = 9(1 - sin^2(x)). Then becomes 12sin^2(x) + sin(x) - 1This is quadratic equation, solved to (4sin(x) -1)(3sin(x) + 1)= 0. Therefore X= sin^-1(1/4) and X=sin^-1(-1/3). X=14.48, 165.52 and X=-19.47, -160.53Question states X=2O-30. To solve for O (4sin(2O-30) - 1)(3sin(2O-30) + 1)so 2O - 30 = 14.48, 165.52, -19.47, -160.53Smallest positive value 2O-30= -19.472O = 10.53, Therefore O = 5.26