Trigonometry Examples

Simplify (sin(x)^2)/(cos(x)^2)-1/(cos(x)^2)
Step 1
Rewrite as .
Step 2
Rewrite as .
Step 3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 4
Simplify terms.
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Step 4.1
Simplify each term.
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Step 4.1.1
Convert from to .
Step 4.1.2
Convert from to .
Step 4.2
Simplify each term.
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Step 4.2.1
Convert from to .
Step 4.2.2
Convert from to .
Step 5
Expand using the FOIL Method.
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Step 5.1
Apply the distributive property.
Step 5.2
Apply the distributive property.
Step 5.3
Apply the distributive property.
Step 6
Simplify terms.
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Step 6.1
Combine the opposite terms in .
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Step 6.1.1
Reorder the factors in the terms and .
Step 6.1.2
Add and .
Step 6.1.3
Add and .
Step 6.2
Simplify each term.
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Step 6.2.1
Multiply .
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Step 6.2.1.1
Raise to the power of .
Step 6.2.1.2
Raise to the power of .
Step 6.2.1.3
Use the power rule to combine exponents.
Step 6.2.1.4
Add and .
Step 6.2.2
Rewrite using the commutative property of multiplication.
Step 6.2.3
Multiply .
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Step 6.2.3.1
Raise to the power of .
Step 6.2.3.2
Raise to the power of .
Step 6.2.3.3
Use the power rule to combine exponents.
Step 6.2.3.4
Add and .
Step 6.3
Simplify with factoring out.
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Step 6.3.1
Reorder and .
Step 6.3.2
Factor out of .
Step 6.3.3
Factor out of .
Step 6.3.4
Factor out of .
Step 7
Apply pythagorean identity.
Step 8
Multiply by .