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 one billion eight hundred eleven million four hundred fifteen thousand two hundred eighty

Interesting facts

  • 1811415280 has 128 divisors, whose sum is 11651671152
  • The reverse of 1811415280 is 0825141181
  • Previous prime number is 17

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 31
  • Digital Root 4

Name

Name one billion seven hundred seventy-one million three hundred seventy-eight thousand six hundred sixty-seven

Interesting facts

  • 1771378667 has 16 divisors, whose sum is 1872383040
  • The reverse of 1771378667 is 7668731771
  • Previous prime number is 397

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 53
  • Digital Root 8

Name

Name one billion nine hundred sixty-one million four hundred seventy-nine thousand five hundred eighty-four

Interesting facts

  • 1961479584 has 256 divisors, whose sum is 19989934272
  • The reverse of 1961479584 is 4859741691
  • Previous prime number is 153

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 54
  • Digital Root 9