Solve for x tan(x)^2-1=0

Problem

tan2(x)−1=0

Solution

1. Isolate the squared trigonometric term by adding 1 to both sides of the equation.

tan2(x)=1

2. Take the square root of both sides, remembering to include both the positive and negative roots.

tan(x)=±√(,1)

tan(x)=±1

3. Identify the angles in the unit circle where the tangent function equals 1 or −1

tan(x)=1⇒x=π/4+n*π

tan(x)=−1⇒x=(3*π)/4+n*π

4. Combine the solutions into a single general expression, noting that the values occur every π/2 radians.

x=π/4+(n*π)/2

Final Answer

tan2(x)−1=0⇒x=π/4+(n*π)/2

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