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Mashcka [7]
3 years ago
13

What are all the exact solutions of -3tan^2x+1=0? Give your answers in radians.

Mathematics
1 answer:
-BARSIC- [3]3 years ago
8 0

Answer:

x = π n_1 + π/6 for n_1 element Z

or x = π n_2 - π/6 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 - 3 tan^2(x) = 0

Subtract 1 from both sides:

-3 tan^2(x) = -1

Divide both sides by -3:

tan^2(x) = 1/3

Take the square root of both sides:

tan(x) = 1/sqrt(3) or tan(x) = -1/sqrt(3)

Take the inverse tangent of both sides:

x = π n_1 + π/6 for n_1 element Z

or tan(x) = -1/sqrt(3)

Take the inverse tangent of both sides:

Answer:  x = π n_1 + π/6 for n_1 element Z

or x = π n_2 - π/6 for n_2 element Z

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Step-by-step explanation:

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