# Verify the Identity 1/(1+cos(x))-1/(1-cos(x))=-2csc(x)cot(x)

Verify the Identity 1/(1+cos(x))-1/(1-cos(x))=-2csc(x)cot(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 .
Subtract from .
Subtract from .
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.
Move the negative in front of the fraction.
Now consider the right side of the equation.
Convert to sines and cosines.
Apply the reciprocal identity to .
Write in sines and cosines using the quotient identity.
Simplify.
Combine and .
Move the negative in front of the fraction.
Multiply .
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.