Trigonometry Examples

Start on the right side.
Factor out of .
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Reorder and .
Factor out of .
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Factor out of .
Move .
Multiply by to get .
Factor out of .
Multiply by to get .
Apply Pythagorean identity in reverse.
Factor.
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Apply Pythagorean identity in reverse.
Simplify.
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Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
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Simplify each term.
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Multiply by to get .
Multiply by to get .
Multiply by to get .
Move .
Use the power rule to combine exponents.
Add and to get .
Add and to get .
Add and to get .
Simplify each term.
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Apply the distributive property.
Multiply by to get .
Simplify .
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Multiply by to get .
Multiply by to get .
Remove unnecessary parentheses.
Subtract from to get .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
Now consider the left side of the equation.
Simplify.
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Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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