Trigonometry Examples

Simplify (sec(x)^4-tan(x)^4)/(sec(x)^2+tan(x)^2)
Step 1
Simplify the numerator.
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Step 1.1
Rewrite as .
Step 1.2
Rewrite as .
Step 1.3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.4
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2
Cancel the common factor of .
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Step 2.1
Cancel the common factor.
Step 2.2
Divide by .
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 terms.
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Step 4.1
Combine the opposite terms in .
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Step 4.1.1
Reorder the factors in the terms and .
Step 4.1.2
Add and .
Step 4.1.3
Add and .
Step 4.2
Simplify each term.
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Step 4.2.1
Multiply .
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Step 4.2.1.1
Raise to the power of .
Step 4.2.1.2
Raise to the power of .
Step 4.2.1.3
Use the power rule to combine exponents.
Step 4.2.1.4
Add and .
Step 4.2.2
Rewrite using the commutative property of multiplication.
Step 4.2.3
Multiply .
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Step 4.2.3.1
Raise to the power of .
Step 4.2.3.2
Raise to the power of .
Step 4.2.3.3
Use the power rule to combine exponents.
Step 4.2.3.4
Add and .
Step 5
Apply pythagorean identity.