Answer:
θ = 94.1 , 145.9 degrees.
Explanation:
2 cos(2θ + 30) = - tan(2θ + 30)
Divide both sides by tan(2θ + 30)
2 cos(2θ + 30)cot(2θ + 30) = -1
cos(2θ + 30)cot(2θ + 30) = -1/2
cos(2θ + 30)cot(2θ + 30) + 1/2 = 0
2(cos(2θ + 30)cot(2θ + 30) + 1) = 0
cos(2θ + 30)cot(2θ + 30) + 1 = 0
Let 2θ + 30 = X, then:
cos X cot X + 1 = 0
cos X * cos X / sin x + 1 = 0
cos^2 X / sin X + 1 = 0
(1 - sin^2 X) sin X + 1 = 0
1 - sin^2x + sin X = 0
sin^2 X - sin X - 1 = 0
sin X = 1.618, -0.618 (using the quadratic formula)
This gives X = 218.17, 321.83 degrees
So
2θ + 30 = 218.17
2θ = 188.17
θ = 94.085
and
2θ + 30 = 321.83
2θ = 291.83
θ = 145.915