Divide each term in the equation by .

Convert from to .

Cancel the common factor.

Divide by .

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

The exact value of is .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Multiply .

Multiply and .

Multiply by .

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.

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.

Add and .

Reorder and .

Add and .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply and .

Multiply by .

The period of the function can be calculated using .

Replace with in the formula for period.

The absolute value is the distance between a number and zero. The distance between and is .

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 x sin(2x)=cos(2x)