# Verify the Identity (csc(x)) divide(sec(x)) plus(cos(x)) divide(sin(x)) equals two cot(x)

Start on the left side.

Apply the reciprocal identity to .

Apply the reciprocal identity to .

Clarify each term.

First, multiply the numerator by the denominator's reciprocal.

Add and .

Add numerators over the common denominator.

Add and .

Now consider the right side of the equation.

Write in sines and cosines using the quotient identity.

Combine and .

Because the two sides have been shown to be equivalent, the equation is an identity.

is an identity

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