Verify the Identity tan(A)=tan(A)*csc(A)^2+cot(-A)

Verify the Identity tan(A)=tan(A)*csc(A)^2+cot(-A)
Start on the right side.
Since is an odd function, rewrite as .
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
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Write in sines and cosines using the quotient identity.
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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Apply the distributive property.
Multiply by .
Combine.
Simplify each term.
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Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Subtract from .
Divide by .
Add 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 four hundred sixteen million eight hundred thirty-five thousand seven hundred eighty-five

Interesting facts

  • 1416835785 has 16 divisors, whose sum is 2282155200
  • The reverse of 1416835785 is 5875386141
  • Previous prime number is 149

Basic properties

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

Name

Name one hundred thirty million eight hundred ten thousand three hundred fifty-five

Interesting facts

  • 130810355 has 16 divisors, whose sum is 159060000
  • The reverse of 130810355 is 553018031
  • Previous prime number is 499

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 26
  • Digital Root 8

Name

Name six hundred seventy-six million seven hundred thirty-six thousand eight hundred eighty-six

Interesting facts

  • 676736886 has 32 divisors, whose sum is 1560526848
  • The reverse of 676736886 is 688637676
  • Previous prime number is 113

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 57
  • Digital Root 3