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

Verify the Identity (1-cos(x))/(sin(x))+(sin(x))/(1-cos(x))=2csc(x)
Start on the left side.
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 each term.
Simplify denominator.
Apply the distributive property.
Multiply by .
Simplify each term.
Apply pythagorean identity.
Simplify.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Factor out of .
Factor out of .
Cancel the common factor of .
Now consider the right side of the equation.
Apply the reciprocal identity to .
Combine and .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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