Solve for x tan(2x)=-1

Problem

tan(2*x)=−1

Solution

1. Identify the general solution for the tangent function. The equation tan(θ)=a has solutions θ=arctan(a)+n*π where n is any integer.

2. Determine the principal value for the inverse tangent. Since tan(−π/4)=−1 we use −π/4 as the principal angle.

3. Set up the equation for the argument 2*x based on the general solution.

2*x=−π/4+n*π

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

x=(−π/4+n*π)/2

5. Simplify the expression to find the final general solution for x

x=−π/8+(n*π)/2

Final Answer

tan(2*x)=−1⇒x=−π/8+(n*π)/2

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