Verify the Identity 1/(1-sin(x))+1/(1+sin(x))=2sec(x)^2

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 .
Subtract from .
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.
Now consider the right side of the equation.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the product rule to .
Simplify.
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One to any power is one.
Combine and .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity 1/(1-sin(x))+1/(1+sin(x))=2sec(x)^2

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