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

Verify the Identity 2cot(x)csc(x)=1/(sec(x)-1)+1/(sec(x)+1)
Start on the right 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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Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify numerator.
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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.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Write in sines and cosines using the quotient identity.
Apply the product rule to .
Simplify.
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Multiply the numerator by the reciprocal of the denominator.
Combine and .
Combine.
Cancel the common factor of and .
Rewrite as .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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Name

Name one billion five million seven hundred fifty-one thousand five hundred ninety-seven

Interesting facts

  • 1005751597 has 4 divisors, whose sum is 1012987360
  • The reverse of 1005751597 is 7951575001
  • Previous prime number is 139

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 40
  • Digital Root 4

Name

Name nine hundred seventeen million two hundred sixty-three thousand seven hundred twenty-three

Interesting facts

  • 917263723 has 4 divisors, whose sum is 924486400
  • The reverse of 917263723 is 327362719
  • Previous prime number is 127

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 40
  • Digital Root 4

Name

Name one billion one hundred eighty-nine million three hundred eighteen thousand nine hundred fifteen

Interesting facts

  • 1189318915 has 8 divisors, whose sum is 1429072560
  • The reverse of 1189318915 is 5198139811
  • Previous prime number is 757

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 46
  • Digital Root 1