Verify the Identity csc(x) to the power of four minus csc(x) to the power of two equals cot(x) to the power of four plus cot(x) to the power of two

Verify the Identity csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2
Start on the right side.
Factor out of .
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Factor out of .
First, multiply by .
Factor out of .
Apply Pythagorean identity.
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Should be rewritten terms.
Apply pythagorean identity.
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
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One raised to any power equals one.
One to any power is one.
Use the distributive law.
Multiply .
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Multiply and .
Multiply by by adding the exponents.
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Apply the power rule to Add exponents.
Add and .
Rewrite as .
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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Add.
Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Add and .
Add numerators over the common denominator.
Clarify the numerator.
Now consider the left side of the equation.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
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Clarify each term.
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One to any power is one.
One to any power is one.
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.
Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Add and .
Combine the numerators over the common denominator.
Clarify the numerator.
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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