Verify the Identity (tan(x))/(1-tan(x)^2)=(sin(x)cos(x))/(2cos(x)^2-1)

Verify the Identity (tan(x))/(1-tan(x)^2)=(sin(x)cos(x))/(2cos(x)^2-1)
Start on the left side.
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
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Write in sines and cosines using the quotient identity.
Apply the reciprocal identity to .
Apply the product rule to .
Simplify.
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Multiply the numerator by the reciprocal of the denominator.
One to any power is one.
Simplify the denominator.
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Apply the distributive property.
Multiply by .
Add and .
To write as a fraction with a common denominator, multiply by .
Combine the numerators over the common denominator.
Combine.
Multiply by .
Combine and .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Combine and .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Write as a fraction with denominator .
Combine.
Remove parentheses.
Multiply by .
Move the negative in front of the fraction.
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 nine hundred twenty-five million eight hundred eighty-two thousand three hundred forty-six

Interesting facts

  • 1925882346 has 16 divisors, whose sum is 3853665504
  • The reverse of 1925882346 is 6432885291
  • Previous prime number is 2053

Basic properties

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

Name

Name one billion five hundred ninety-three million seven hundred forty-seven thousand four hundred twenty-four

Interesting facts

  • 1593747424 has 128 divisors, whose sum is 12213578520
  • The reverse of 1593747424 is 4247473951
  • Previous prime number is 109

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 46
  • Digital Root 1

Name

Name one hundred fifty-eight million seven hundred seventy-five thousand two hundred two

Interesting facts

  • 158775202 has 8 divisors, whose sum is 238289436
  • The reverse of 158775202 is 202577851
  • Previous prime number is 1973

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 37
  • Digital Root 1