Take the inverse tangent of both sides of the equation to extract from inside the tangent.

The exact value of is .

Subtract from both sides of the equation.

Simplify the right side of the equation.

To write as a fraction with a common denominator, multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of .

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Multiply both sides of the equation by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.

Simplify .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of .

Add and .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Simplify the right side of the equation.

To write as a fraction with a common denominator, multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Multiply by .

Subtract from .

Multiply both sides of the equation by .

Simplify both sides of the equation.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

The period of the function can be calculated using .

Replace with in the formula for period.

Solve the equation.

is approximately which is positive so remove the absolute value

Multiply the numerator by the reciprocal of the denominator.

Move to the left of .

Add to to find the positive angle.

To write as a fraction with a common denominator, multiply by .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

List the new angles.

The period of the function is so values will repeat every radians in both directions.

, for any integer

Consolidate the answers.

, for any integer

Solve for ? tan(x/2+pi/3)=1