Verify the Identity cos(x)^4-sin(x)^4=1-2sin(x)^2

Math
Start on the left side.
Factor.
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Rewrite as .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify.
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Apply pythagorean identity.
Multiply by .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Apply the distributive property.
Simplify.
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Simplify each term.
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Apply the distributive property.
Multiply .
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Apply the distributive property.
Multiply .
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Simplify each term.
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Move to the left of .
Rewrite as .
Subtract from .
Add and .
Apply Pythagorean identity in reverse.
Subtract from .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity cos(x)^4-sin(x)^4=1-2sin(x)^2

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