Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Set the first factor equal to .

Subtract from both sides of the equation.

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

Evaluate .

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

Simplify the expression to find the second solution.

Simplify .

Multiply by .

Subtract from .

Add to .

The resulting angle of is positive and coterminal with .

Find the period.

The period of the function can be calculated using .

Replace with in the formula for period.

Solve the equation.

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

Divide by .

Add to every negative angle to get positive angles.

Add to to find the positive angle.

Replace with decimal approximation.

Subtract from .

List the new angles.

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

, for any integer

, for any integer

Set the next factor equal to .

Add to both sides of the equation.

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

Evaluate .

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

Simplify the expression to find the second solution.

Remove the parentheses around the expression .

Add and .

Find the period.

The period of the function can be calculated using .

Replace with in the formula for period.

Solve the equation.

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

Divide by .

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

, for any integer

Consolidate the answers.

, for any integer

, for any integer

Set the next factor equal to .

Subtract from both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

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

The exact value of is .

The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third 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.

Multiply by .

Subtract from .

Find the period.

The period of the function can be calculated using .

Replace with in the formula for period.

Solve the equation.

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

Divide by .

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

, for any integer

, for any integer

The final solution is all the values that make true.

, for any integer

Solve for ? (tan(x)^2-9)(2cos(x)+1)=0