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

Verify the Identity (1-cos(x))/(sin(x))+(sin(x))/(1-cos(x))=2csc(x)
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 each term.
Simplify denominator.
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Apply the distributive property.
Multiply by .
Simplify each term.
Apply pythagorean identity.
Simplify.
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Simplify the numerator.
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Add and .
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
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Multiply by .
Factor out of .
Factor out of .
Cancel the common factor of .
Now consider the right side of the equation.
Apply the reciprocal identity to .
Combine and .
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 four hundred sixty-seven million four hundred forty-two thousand five hundred seventy-three

Interesting facts

  • 1467442573 has 16 divisors, whose sum is 1554973056
  • The reverse of 1467442573 is 3752447641
  • Previous prime number is 83

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7

Name

Name one billion three hundred fifty-two million three hundred fifty-eight thousand eight hundred seventy-two

Interesting facts

  • 1352358872 has 32 divisors, whose sum is 4626736632
  • The reverse of 1352358872 is 2788532531
  • Previous prime number is 73

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 44
  • Digital Root 8

Name

Name nine hundred forty-eight million four hundred forty-three thousand six hundred ninety-four

Interesting facts

  • 948443694 has 8 divisors, whose sum is 1465776720
  • The reverse of 948443694 is 496344849
  • Previous prime number is 33

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 51
  • Digital Root 6