# Verify the Identity cot(x)sec(x)^4=cot(x)+2tan(x)+tan(x)^3

Start on the right side.
Convert to sines and cosines.
Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Apply the product rule to .
Simplify.
Combine and .
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.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
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.
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply pythagorean identity.
One to any power is one.
Now consider the left side of the equation.
Convert to sines and cosines.
Write in sines and cosines using the quotient identity.
Apply the reciprocal identity to .
Apply the product rule to .
Simplify.
One to any power is one.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply and .
Reorder terms.
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity cot(x)sec(x)^4=cot(x)+2tan(x)+tan(x)^3