Solve for x tan(2x)=- square root of 3

Problem

tan(2*x)=−√(,3)

Solution

1. Identify the reference angle for the tangent function where the value is √(,3)

tan(θ)=√(,3)⇒θ=π/3

2. Determine the general solution for the tangent equation tan(θ)=y

θ=arctan(y)+n*π

3. Substitute the given value into the general solution formula, noting that arctan(−√(,3))=−π/3

2*x=−π/3+n*π

4. Isolate x by dividing the entire equation by 2

x=−π/6+(n*π)/2

Final Answer

tan(2*x)=−√(,3)⇒x=−π/6+(n*π)/2

Want more problems? Check here!