Verify the Identity cot(x)(cot(x)+tan(x))=csc(x)^2
Start on the left side.
Apply the distributive property.
Multiply .
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
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Apply the reciprocalidentity to .
Write in sines and cosines using the quotientidentity.
Write in sines and cosines using the quotientidentity.
Apply the product rule to .
Simplify.
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Simplify each term.
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One to any power is one.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Add and .
Add and .
Now consider the right side of the equation.
Convert to sines and cosines.
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Apply the reciprocalidentity to .
Apply the product rule to .
One to any power is one.
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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