Start on the left side.

Rewrite as .

Rewrite as .

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

Simplify.

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 each term.

Apply the distributive property.

Multiply .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Apply the distributive property.

Multiply .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify each term.

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