# Verify the Identity (cot(B)^2-cos(B)^2)/(csc(B)^2-1)=cos(B)^2

Verify the Identity (cot(B)^2-cos(B)^2)/(csc(B)^2-1)=cos(B)^2
Start on the left side.
Convert to sines and cosines.
Write in sines and cosines using the quotient identity.
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule 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 .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Factor out of .
Multiply by .
Factor out of .
Factor out of .
Move to the left of .
Rewrite as .
Rewrite in a factored form.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify the denominator.
One to any power is one.
Move to the left of .
Rewrite as .
Rewrite in a factored form.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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