Verify the Identity 1/(cos(x)+1)+1/(cos(x)-1)=-2csc(x)cot(x)

Math
Start on the left side.
Add fractions.
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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.
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify numerator.
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Simplify each term.
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Multiply by .
Multiply by .
Add and .
Add and .
Add and .
Simplify denominator.
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Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Apply Pythagorean identity.
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Reorder and .
Rewrite as .
Factor out of .
Factor out of .
Rewrite as .
Apply pythagorean identity.
Move the negative in front of the fraction.
Now consider the right side of the equation.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Write in sines and cosines using the quotient identity.
Simplify.
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Combine and .
Move the negative in front of the fraction.
Multiply .
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Move to the left of .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity 1/(cos(x)+1)+1/(cos(x)-1)=-2csc(x)cot(x)

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