# Verify the Identity (tan(x)^2+1)(cos(x)^2-1)=-tan(x)^2

Start on the left side.

Apply pythagorean identity.

Reorder and .

Rewrite as .

Factor out of .

Factor out of .

Rewrite as .

Apply pythagorean identity.

Apply the reciprocal identity to .

Apply the product rule to .

One to any power is one.

Combine and .

Rewrite as .

Because the two sides have been shown to be equivalent, the equation is an identity.

is an identity

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