# Verify the Identity (sec(x)-csc(x))/(sec(x)+csc(x))=(tan(x)-1)/(tan(x)+1)

Start on the left side.
Convert to sines and cosines.
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Simplify.
Multiply the numerator and denominator of the complex fraction by .
Multiply by .
Combine.
Apply the distributive property.
Simplify by cancelling.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Now consider the right side of the equation.
Convert to sines and cosines.
Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Simplify.
Multiply the numerator and denominator of the complex fraction by .
Multiply by .
Combine.
Apply the distributive property.
Simplify by cancelling.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Move to the left of .
Rewrite as .
Multiply by .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity (sec(x)-csc(x))/(sec(x)+csc(x))=(tan(x)-1)/(tan(x)+1)