# Verify the Identity (csc(x))/(cot(x)+tan(x))=cos(x)

Start on the left side.
Convert to sines and cosines.
Apply the reciprocal identity to .
Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Simplify.
Multiply the numerator by the reciprocal of the denominator.
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 .
Cancel the common factor of .
Apply pythagorean identity.
Divide by .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity (csc(x))/(cot(x)+tan(x))=cos(x)

Scroll to top