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

Problem

3*tan(x)=tan(x)

Solution

1. Rearrange the equation to set it equal to zero by subtracting tan(x) from both sides.

3*tan(x)−tan(x)=0

2. Factor out the greatest common factor, which is tan(x)

tan(x)*(3*tan(x)−1)=0

3. Apply the zero product property to set each factor equal to zero.

tan(x)=0

3*tan(x)−1=0

4. Solve the first equation for x

x=n*π

5. Isolate the squared term in the second equation.

3*tan(x)=1

tan(x)=1/3

6. Take the square root of both sides to find the values for tan(x)

tan(x)=±√(,1/3)

tan(x)=±1/√(,3)

7. Solve for x using the unit circle or inverse tangent values.

x=π/6+n*π

x=(5*π)/6+n*π

8. Combine all solutions into a general form where n is any integer.

x=n*π,π/6+n*π,(5*π)/6+n*π

Final Answer

x=n*π,π/6+n*π,(5*π)/6+n*π

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