# Verify the Identity 1/(tan(x)+cot(x))=sin(x)cos(x) Start on the left side.
Convert to sines and cosines.
Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Simplify.
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.
Multiply .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
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
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