Find the solution set of the equation 7tanθ = 2√3 + tanθ

Question

I think that the solution set is {30°} but I’m not sure how to solve the equation since we only discussed as to how (cosineθ, sineθ) = (x, y).

Answer 1

Simplifying the equation:

6tan(θ) = 2√3

Solving for tan(θ):

tan(θ) = 2√3/6 = √3/3

Since the tangent is positive, then θ can be in either Quadrant I or III. So θ can be 30° or 210°.

Also, it would repeat every 30° + 180°n as you continue to loop around the unit circle for n = 0,1,2,....

Answer 2