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

Verify the Identity (tan(x)^2+1)(cos(x)^2-1)=-tan(x)^2
Start on the left side.
Apply Pythagorean identity.
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Apply pythagorean identity.
Reorder and .
Rewrite as .
Factor out of .
Factor out of .
Rewrite as .
Apply pythagorean identity.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the product rule to .
Simplify.
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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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