Rewrite as .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Apply pythagorean identity.

Multiply by .

Apply the cosine double–angle identity.

Simplify cos(x)^4-sin(x)^4

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# Simplify cos(x)^4-sin(x)^4

Rewrite as .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Apply pythagorean identity.

Multiply by .

Apply the cosine double–angle identity.

Simplify cos(x)^4-sin(x)^4