Precalculus Examples

Verify the Identity (cot(x)-csc(x))(cos(x)+1)=-sin(x)
Step 1
Start on the left side.
Step 2
Simplify the expression.
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Step 2.1
Simplify each term.
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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.
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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.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Multiply .
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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 .
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Step 2.11.1
Factor out of .
Step 2.11.2
Cancel the common factors.
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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