Question

Which of the following is a solution to
`tanx+√3 =0`60150240300

a) x= π/6
b) x= π/3
c) x= 2π/3
d) x= 5π/6
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Answer 1

To find the solution to the equation tan(x) + √3 = 0, we identify that tan(x) must be negative and equal to -√3. The angle in the second quadrant with the tangent value of √3 is 5π/6. Thus, the correct answer is d) x = 5π/6.

Step-by-step explanation:

The question asks to find a solution to the equation tan(x) + √3 = 0. To solve for x, we first isolate the tangent function:

tan(x) = -√3

This equation implies that the tangent of x must equal to the negative square root of three. We are looking for an angle where tangent is negative and its absolute value is the square root of 3. The tangent function is negative in the second and fourth quadrants. Since √3 corresponds to the tangent of π/3, we know x must be an angle in the second quadrant that has the same reference angle as π/3. Therefore, the angle that satisfies this condition is x = 5π/6. Among the provided options, the correct choice is d) x = 5π/6.