Verify the Identity 1/(1-sin(x))-1/(1+sin(x))=2tan(x)sec(x)

Start on the left side.
Subtract fractions.
To write as a fraction with a common denominator, multiply by .
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.
Combine.
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify numerator.
Simplify each term.
Multiply by .
Apply the distributive property.
Multiply by .
Multiply .
Multiply by .
Multiply by .
Subtract from .
Simplify denominator.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Apply pythagorean identity.
Now consider the right side of the equation.
Convert to sines and cosines.
Write in sines and cosines using the quotient identity.
Apply the reciprocal identity to .
Simplify.
Combine and .
Multiply .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity 1/(1-sin(x))-1/(1+sin(x))=2tan(x)sec(x)