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

Problem

tan(x)−1=0

Solution

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

tan(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 reference angle where the tangent function equals 1.

x=π/4

4. Determine all solutions within one period of the tangent function, which is (−π/2,π/2)

x=π/4

x=−π/4

5. Generalize the solution by adding the period of the tangent function, n*π where n is any integer.

x=π/4+n*π

x=−π/4+n*π

6. Combine the solutions into a single expression for simplicity.

x=π/4+(n*π)/2

Final Answer

tan(x)−1=0⇒x=π/4+(n*π)/2

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