# Verify the Identity 1+sec(x)^2sin(x)^2=sec(x)^2 Start on the left side.
Convert to sines and cosines.
Apply the reciprocal identity to .
Simplify.
Apply the product rule to .
One to any power is one.
Write as a fraction with denominator .
Combine.
Multiply by .
Multiply by .
Apply Pythagorean identity in reverse.
Simplify.
Simplify the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Now consider the right side of the equation.
Convert to sines and cosines.
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
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