Start on the left side.

Write in sines and cosines using the quotient identity.

Write in sines and cosines using the quotient identity.

Simplify the denominator.

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.

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Apply pythagorean identity.

Divide by .

Rewrite as .

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

is an identity

Verify the Identity 1/(tan(x)+cot(x))=sin(x)cos(x)