Verify the Identity cot(x)(cot(x)+tan(x))=csc(x)^2

Verify the Identity cot(x)(cot(x)+tan(x))=csc(x)^2
Start on the left side.
Apply the distributive property.
Multiply .
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Apply the product rule to .
Simplify.
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Simplify each term.
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One to any power is one.
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.
Add and .
Add and .
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 .
One to any power is one.
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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Name

Name four hundred ninety-five million seven hundred ninety-eight thousand four hundred fifty-seven

Interesting facts

  • 495798457 has 16 divisors, whose sum is 619517952
  • The reverse of 495798457 is 754897594
  • Previous prime number is 463

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 58
  • Digital Root 4

Name

Name one billion eight hundred eighty-six million four hundred ninety-three thousand nine hundred twelve

Interesting facts

  • 1886493912 has 64 divisors, whose sum is 8523071424
  • The reverse of 1886493912 is 2193946881
  • Previous prime number is 251

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 51
  • Digital Root 6

Name

Name one billion five hundred eighteen million eight hundred nineteen thousand five hundred twenty-eight

Interesting facts

  • 1518819528 has 32 divisors, whose sum is 6834687984
  • The reverse of 1518819528 is 8259188151
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 48
  • Digital Root 3