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Precalculus Examples
Step 1
Start on the left side.
Step 2
Step 2.1
Simplify each term.
Step 2.1.1
Rewrite in terms of sines and cosines.
Step 2.1.2
Rewrite in terms of sines and cosines.
Step 2.2
Expand using the FOIL Method.
Step 2.2.1
Apply the distributive property.
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Apply the distributive property.
Step 2.3
Simplify and combine like terms.
Step 2.3.1
Simplify each term.
Step 2.3.1.1
Multiply .
Step 2.3.1.1.1
Combine and .
Step 2.3.1.1.2
Raise to the power of .
Step 2.3.1.1.3
Raise to the power of .
Step 2.3.1.1.4
Use the power rule to combine exponents.
Step 2.3.1.1.5
Add and .
Step 2.3.1.2
Multiply by .
Step 2.3.1.3
Combine and .
Step 2.3.1.4
Multiply by .
Step 2.3.2
Subtract from .
Step 2.3.3
Add and .
Step 2.4
Combine the numerators over the common denominator.
Step 2.5
Reorder and .
Step 2.6
Rewrite as .
Step 2.7
Factor out of .
Step 2.8
Factor out of .
Step 2.9
Rewrite as .
Step 2.10
Apply pythagorean identity.
Step 2.11
Cancel the common factor of and .
Step 2.11.1
Factor out of .
Step 2.11.2
Cancel the common factors.
Step 2.11.2.1
Multiply by .
Step 2.11.2.2
Cancel the common factor.
Step 2.11.2.3
Rewrite the expression.
Step 2.11.2.4
Divide by .
Step 3
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity