Trigonometry Examples

Simplify (cos(t)-sec(t))^2
Step 1
Rewrite in terms of sines and cosines.
Step 2
Rewrite as .
Step 3
Expand using the FOIL Method.
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Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 4
Simplify and combine like terms.
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Step 4.1
Simplify each term.
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Step 4.1.1
Multiply .
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Step 4.1.1.1
Raise to the power of .
Step 4.1.1.2
Raise to the power of .
Step 4.1.1.3
Use the power rule to combine exponents.
Step 4.1.1.4
Add and .
Step 4.1.2
Rewrite using the commutative property of multiplication.
Step 4.1.3
Cancel the common factor of .
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Step 4.1.3.1
Factor out of .
Step 4.1.3.2
Cancel the common factor.
Step 4.1.3.3
Rewrite the expression.
Step 4.1.4
Cancel the common factor of .
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Step 4.1.4.1
Move the leading negative in into the numerator.
Step 4.1.4.2
Cancel the common factor.
Step 4.1.4.3
Rewrite the expression.
Step 4.1.5
Multiply .
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Step 4.1.5.1
Multiply by .
Step 4.1.5.2
Multiply by .
Step 4.1.5.3
Multiply by .
Step 4.1.5.4
Raise to the power of .
Step 4.1.5.5
Raise to the power of .
Step 4.1.5.6
Use the power rule to combine exponents.
Step 4.1.5.7
Add and .
Step 4.2
Subtract from .
Step 5
Simplify each term.
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Step 5.1
Rewrite as .
Step 5.2
Rewrite as .
Step 5.3
Convert from to .