Solve the question for exact solutions in the interval [0,360) degrees. Use an algebraic method

Question

9sec^2 theta tan theta = 12 tan theta

what is the solution set{ }

Answer 1

Replace sec²x with (tan²x + 1).

So 9(tan²x + 1) tanx = 12tanx

Distribute the 9 and tanx:

9tan³x + 9tanx = 12tanx

9tan³x - 3tanx = 0

Factor:

3tanx(3tan²x = 1) = 0.

So, tanx = 0 or tan²x = 1/3

Solve each of the above equations by using arctan (for 2nd equation tanx = ±√1/3

To see the answers (in radians), attach the following to the URL for Desmos online graphing calculator.

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