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

Math
Start on the left side.
Convert to sines and cosines.
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Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Simplify.
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Simplify the denominator.
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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 .
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Combine.
Combine.
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply .
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply .
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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)

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