Solve for x y=tan(2x)

Problem

y=tan(2*x)

Solution

1. Identify the goal as solving for x in terms of y to find the inverse relationship.

2. Apply the arctangent function to both sides of the equation to isolate the argument of the tangent function.

arctan(y)=arctan(tan(2*x))

3. Simplify the right side using the property that arctan(tan(θ))=θ within the appropriate domain.

arctan(y)=2*x

4. Isolate x by dividing both sides of the equation by 2

x=arctan(y)/2

Final Answer

x=1/2*arctan(y)

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