Trigonometry Examples

Simplify (sec(x)-cos(x))^2-(sec(x)+cos(x))^2
Step 1
Simplify each term.
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Step 1.1
Rewrite in terms of sines and cosines.
Step 1.2
Rewrite as .
Step 1.3
Expand using the FOIL Method.
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Step 1.3.1
Apply the distributive property.
Step 1.3.2
Apply the distributive property.
Step 1.3.3
Apply the distributive property.
Step 1.4
Simplify and combine like terms.
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Step 1.4.1
Simplify each term.
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Step 1.4.1.1
Multiply .
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Step 1.4.1.1.1
Multiply by .
Step 1.4.1.1.2
Raise to the power of .
Step 1.4.1.1.3
Raise to the power of .
Step 1.4.1.1.4
Use the power rule to combine exponents.
Step 1.4.1.1.5
Add and .
Step 1.4.1.2
Rewrite using the commutative property of multiplication.
Step 1.4.1.3
Cancel the common factor of .
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Step 1.4.1.3.1
Move the leading negative in into the numerator.
Step 1.4.1.3.2
Cancel the common factor.
Step 1.4.1.3.3
Rewrite the expression.
Step 1.4.1.4
Cancel the common factor of .
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Step 1.4.1.4.1
Factor out of .
Step 1.4.1.4.2
Cancel the common factor.
Step 1.4.1.4.3
Rewrite the expression.
Step 1.4.1.5
Multiply .
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Step 1.4.1.5.1
Multiply by .
Step 1.4.1.5.2
Multiply by .
Step 1.4.1.5.3
Raise to the power of .
Step 1.4.1.5.4
Raise to the power of .
Step 1.4.1.5.5
Use the power rule to combine exponents.
Step 1.4.1.5.6
Add and .
Step 1.4.2
Subtract from .
Step 1.5
Rewrite in terms of sines and cosines.
Step 1.6
Rewrite as .
Step 1.7
Expand using the FOIL Method.
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Step 1.7.1
Apply the distributive property.
Step 1.7.2
Apply the distributive property.
Step 1.7.3
Apply the distributive property.
Step 1.8
Simplify and combine like terms.
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Step 1.8.1
Simplify each term.
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Step 1.8.1.1
Multiply .
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Step 1.8.1.1.1
Multiply by .
Step 1.8.1.1.2
Raise to the power of .
Step 1.8.1.1.3
Raise to the power of .
Step 1.8.1.1.4
Use the power rule to combine exponents.
Step 1.8.1.1.5
Add and .
Step 1.8.1.2
Cancel the common factor of .
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Step 1.8.1.2.1
Cancel the common factor.
Step 1.8.1.2.2
Rewrite the expression.
Step 1.8.1.3
Cancel the common factor of .
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Step 1.8.1.3.1
Cancel the common factor.
Step 1.8.1.3.2
Rewrite the expression.
Step 1.8.1.4
Multiply .
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Step 1.8.1.4.1
Raise to the power of .
Step 1.8.1.4.2
Raise to the power of .
Step 1.8.1.4.3
Use the power rule to combine exponents.
Step 1.8.1.4.4
Add and .
Step 1.8.2
Add and .
Step 1.9
Apply the distributive property.
Step 1.10
Multiply by .
Step 2
Simplify by adding terms.
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Step 2.1
Combine the opposite terms in .
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Step 2.1.1
Subtract from .
Step 2.1.2
Subtract from .
Step 2.1.3
Subtract from .
Step 2.1.4
Add and .
Step 2.2
Subtract from .