Verify the Identity (sec(x)^2)/(sec(x)^2-1)=csc(x)^2

Math
Start on the left side.
Apply pythagorean identity.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Write in sines and cosines using the quotient identity.
Apply the product rule to .
Apply the product rule to .
Simplify.
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Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Combine and .
One to any power is one.
Now consider the right side of the equation.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the product rule to .
One to any power is one.
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity (sec(x)^2)/(sec(x)^2-1)=csc(x)^2

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