# Verify the Identity cos(x)+sin(x)*tan(x)=sec(x)

Start on the left side.
Write in sines and cosines using the quotient identity.
Write as a fraction with denominator .
Combine.
Multiply .
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.
Rewrite as .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity cos(x)+sin(x)*tan(x)=sec(x)