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How many solutions to tan(2x) = √3 are there in the interval [0, 2π]?

a) One solution
b) Two solutions
c) Three solutions
d) Four solutions

1 Answer

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Final answer:

The equation tan(2x) = √3 has two solutions in the interval [0, 2π]: x = π/6 and x = 5π/6.

Step-by-step explanation:

To find the number of solutions to the equation tan(2x) = √3 in the interval [0, 2π], we can use the unit circle and the periodic nature of the tangent function. The equation tan(2x) = √3 has the same solutions as sin(2x)/cos(2x) = √3. From the unit circle, we know that sin(2x) = √3/2 when 2x = π/3 and 5π/3. Therefore, the equation has two solutions in the given interval: x = π/6 and x = 5π/6. The correct answer is b) Two solutions.

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