Solve for x tan(x)+1=0

Problem

tan(x)+1=0

Solution

1. Isolate the trigonometric function by subtracting 1 from both sides of the equation.

tan(x)=−1

2. Identify the reference angle by finding the value of x in the first quadrant where tan(x)=1

(x_ref)=π/4

3. Determine the quadrants where the tangent function is negative, which are Quadrant II and Quadrant IV.

x=π−π/4=(3*π)/4

x=2*π−π/4=(7*π)/4

4. Generalize the solution by adding multiples of the period of the tangent function, which is π

x=(3*π)/4+n*π

Final Answer

tan(x)+1=0⇒x=(3*π)/4+n*π,n∈ℤ

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