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Trigonometry Examples
Step 1
Step 1.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.2
Simplify.
Step 1.2.1
Rewrite in terms of sines and cosines.
Step 1.2.2
Factor out of .
Step 1.2.2.1
Multiply by .
Step 1.2.2.2
Factor out of .
Step 1.2.2.3
Factor out of .
Step 1.2.3
Rewrite in terms of sines and cosines.
Step 1.2.4
Factor out of .
Step 1.2.4.1
Multiply by .
Step 1.2.4.2
Factor out of .
Step 1.2.4.3
Factor out of .
Step 1.2.5
Combine exponents.
Step 1.2.5.1
Raise to the power of .
Step 1.2.5.2
Raise to the power of .
Step 1.2.5.3
Use the power rule to combine exponents.
Step 1.2.5.4
Add and .
Step 2
Step 2.1
Rewrite in terms of sines and cosines.
Step 2.2
Apply the product rule to .
Step 3
Combine and .
Step 4
Step 4.1
Use the power rule to combine exponents.
Step 4.2
Add and .
Step 5
Multiply the numerator by the reciprocal of the denominator.
Step 6
Step 6.1
Factor out of .
Step 6.2
Factor out of .
Step 6.3
Cancel the common factor.
Step 6.4
Rewrite the expression.
Step 7
Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Apply the distributive property.
Step 8
Step 8.1
Simplify each term.
Step 8.1.1
Multiply by .
Step 8.1.2
Multiply by .
Step 8.1.3
Multiply by .
Step 8.1.4
Rewrite using the commutative property of multiplication.
Step 8.1.5
Multiply .
Step 8.1.5.1
Multiply by .
Step 8.1.5.2
Raise to the power of .
Step 8.1.5.3
Raise to the power of .
Step 8.1.5.4
Use the power rule to combine exponents.
Step 8.1.5.5
Add and .
Step 8.2
Add and .
Step 8.3
Add and .
Step 9
Step 9.1
Apply the distributive property.
Step 9.2
Multiply by .
Step 9.3
Cancel the common factor of .
Step 9.3.1
Move the leading negative in into the numerator.
Step 9.3.2
Cancel the common factor.
Step 9.3.3
Rewrite the expression.
Step 9.4
Rewrite as .
Step 9.5
Combine the numerators over the common denominator.
Step 9.6
Reorder and .
Step 9.7
Rewrite as .
Step 9.8
Factor out of .
Step 9.9
Factor out of .
Step 9.10
Rewrite as .
Step 10
Apply pythagorean identity.
Step 11
Step 11.1
Cancel the common factor.
Step 11.2
Divide by .