Question

Which of the following is NOT a solution to (3tan^2x-1)(3tan^2x-3=0

Answer 1

Answer:

120°

Explanation:

It is convenient to evaluate the expression 3tan²(x) for each of the given angles and see which give 1 or 3 as a result. The result for 120° is 9, so that angle will not be a solution to this equation.

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Solutions will be angles that make the factors zero. The first factor is zero when ...

... tan²(x) = 1/3

... x = arctan(±√(1/3)) = ±30° + k·180° for some integer k

Here, the angles of interest are 30°, 150°.

The second factor is zero when ...

... tan²(x) = 1

... x = arctan(±1) = ±45° +k·180° for some integer k

Here, the angles of interest are 225°, 315°.

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Comment on the solution set

The list of all solutions in the range 0–360° will include ...

... {30°, 45°, 135°, 150°, 210°, 225°, 315°, 330°}