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 one hundred seventy million one hundred eleven thousand five hundred sixty-one

Interesting facts

  • 1170111561 has 16 divisors, whose sum is 1645443840
  • The reverse of 1170111561 is 1651110711
  • Previous prime number is 523

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 24
  • Digital Root 6

Name

Name two billion one hundred twenty-six million two hundred twenty-eight thousand ninety

Interesting facts

  • 2126228090 has 32 divisors, whose sum is 4040010000
  • The reverse of 2126228090 is 0908226212
  • Previous prime number is 29

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 32
  • Digital Root 5

Name

Name one billion one hundred forty-two million fifty-nine thousand two hundred twenty-two

Interesting facts

  • 1142059222 has 8 divisors, whose sum is 1713616776
  • The reverse of 1142059222 is 2229502411
  • Previous prime number is 3307

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 28
  • Digital Root 1