# Solve for x 11sin(x)^2=11cos(x)^2

Solve for x 11sin(x)^2=11cos(x)^2
Move to the left side of the equation by subtracting it from both sides.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Divide each term in the equation by .
Replace with an equivalent expression in the numerator.
Remove parentheses.
Rewrite in terms of sines and cosines.
Apply the distributive property.
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Convert from to .
Separate fractions.
Convert from to .
Divide by .
Multiply by .
Subtract from both sides of the equation.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
The exact value of is .
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 .
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 .
Move the negative in front of the fraction.
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.
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 .
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 and solve.
Set the next factor equal to .
Divide each term in the equation by .
Replace with an equivalent expression in the numerator.
Remove parentheses.
Rewrite in terms of sines and cosines.
Apply the distributive property.
Combine and .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Convert from to .
Separate fractions.
Convert from to .
Divide by .
Multiply by .
Add to both sides of the equation.
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
The exact value of is .
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 .
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