Solve for x tan(x)^2=tan(x)

Problem

tan(x)=tan(x)

Solution

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

tan(x)−tan(x)=0

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

tan(x)*(tan(x)−1)=0

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

tan(x)=0

tan(x)−1=0⇒tan(x)=1

4. Solve for x in the first case where tan(x)=0

x=n*π

5. Solve for x in the second case where tan(x)=1

x=π/4+n*π

6. Combine the solutions using the integer n to represent all possible values.

x=n*π,π/4+n*π

Final Answer

tan(x)=tan(x)⇒x=n*π,π/4+n*π

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