Solve for x tan(x/2)=-1

Problem

tan(x/2)=−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 tan(θ)=−1 the principal value is θ=−π/4

3. Set up the equation for the argument. Substitute θ=x/2 into the general solution form:

x/2=−π/4+n*π

4. Isolate the variable x by multiplying both sides of the equation by 2

x=2*(−π/4+n*π)

5. Simplify the expression to find the final general solution:

x=−π/2+2*n*π

Final Answer

tan(x/2)=−1⇒x=−π/2+2*n*π

Want more problems? Check here!