# Verify the Identity (cot(B) to the power of two minus cos(B) to the power of two) divide(csc(B) to the power of two minus one) equals cos(B) to the power of two

Start on the left side.

Write in sines and cosines using the quotient identity.

Apply the reciprocal identity to .

Apply the product rule to .

Apply the product rule to .

First, multiply the numerator and denominator of the complex fraction by .

Multiply by .

Add.

Use the distributive law.

Clarify by cancelling.

The common factor should be canceled of .

Cancel the common factor.

Reformulate the expression.

Cancel the common factor of .

Cancel the common factor.

Should be rewritten the expression.

Clarify 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 .

As both terms are perfect squares, factor using the difference of squares formula, where and .

Clarify the denominator.

One raised to any power equals one.

Move to the left of .

Rewrite as .

Rewrite in a factored form.

Rewrite as .

Because 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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