Verify the Identity (sec(x)-csc(x))/(sec(x)+csc(x))=(tan(x)-1)/(tan(x)+1)

Math
Start on the left side.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Simplify.
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Multiply the numerator and denominator of the complex fraction by .
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Multiply by .
Combine.
Apply the distributive property.
Simplify by cancelling.
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Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Now consider the right side of the equation.
Convert to sines and cosines.
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Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Simplify.
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Multiply the numerator and denominator of the complex fraction by .
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Multiply by .
Combine.
Apply the distributive property.
Simplify by cancelling.
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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.
Simplify the numerator.
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Move to the left of .
Rewrite as .
Multiply by .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity (sec(x)-csc(x))/(sec(x)+csc(x))=(tan(x)-1)/(tan(x)+1)

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