Solve for x tan(x) = square root of 3

Problem

tan(x)=√(,3)

Solution

1. Identify the basic reference angle for the tangent function. We know that tan(π/3)=√(,3) in the first quadrant.

2. Determine the period of the tangent function. The tangent function has a period of π meaning it repeats its values every π units.

3. Apply the general solution formula for the equation tan(x)=a The general solution is x=arctan(a)+n*π where n is any integer.

4. Substitute the known value into the general solution. Since arctan(√(,3))=π/3 the solutions are x=π/3+n*π

Final Answer

tan(x)=√(,3)⇒x=π/3+n*π,n∈ℤ

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