# Trigonometry Examples

Factor out of .
Simplify the denominator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Turn the numerator into a polynomial.
Rewrite.
Apply the distributive property.
Apply the distributive property.
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Turn the denominator into a polynomial.
Rewrite.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by to get .
Reorder and .
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
 + - + - +
Divide the highest order term in the dividend by the highest order term in divisor .
 + + - + - +
Multiply the new quotient term by the divisor.
 + + - + - + + + -
The expression needs to be subtracted from the dividend, so change all the signs in
 + + - + - + - - +
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 + + - + - + - - + + +
Pull the next term from the original dividend down into the current dividend.
 + + - + - + - - + + + +
Divide the highest order term in the dividend by the highest order term in divisor .
 + + + - + - + - - + + + +
Multiply the new quotient term by the divisor.
 + + + - + - + - - + + + + + + -
The expression needs to be subtracted from the dividend, so change all the signs in
 + + + - + - + - - + + + + - - +
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 + + + - + - + - - + + + + - - + + +
The final answer is the quotient plus the remainder over the divisor.

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