Solve for x 3tan(x)^3=tan(x)

Problem

3*tan(x)=tan(x)

Solution

1. Subtract tan(x) from both sides to set the equation to zero.

3*tan(x)−tan(x)=0

2. Factor out the common term tan(x) from the expression.

tan(x)*(3*tan(x)−1)=0

3. Apply the zero product property by setting each factor equal to zero.

tan(x)=0

3*tan(x)−1=0

4. Solve the first equation for x

x=arctan(0)+n*π

x=n*π

5. Isolate tan(x) in the second equation.

3*tan(x)=1

tan(x)=1/3

tan(x)=±1/√(,3)

6. Solve for x using the values where the tangent is ±1/√(,3)

x=±π/6+n*π

Final Answer

x=n*π,π/6+n*π,(5*π)/6+n*π

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