Simplify cos(arctan(x))

Simplify cos(arctan(x))
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
One to any power is one.
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify.
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Name

Name twenty million seven hundred fifty-one thousand four hundred thirty-four

Interesting facts

  • 20751434 has 16 divisors, whose sum is 34032096
  • The reverse of 20751434 is 43415702
  • Previous prime number is 661

Basic properties

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

Name

Name one hundred sixty-four million seven hundred seventy-five thousand two hundred seventy-seven

Interesting facts

  • 164775277 has 16 divisors, whose sum is 177049600
  • The reverse of 164775277 is 772577461
  • Previous prime number is 151

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1

Name

Name one billion two hundred thirty-nine million six hundred forty-nine thousand four hundred eighty-eight

Interesting facts

  • 1239649488 has 512 divisors, whose sum is 9797760000
  • The reverse of 1239649488 is 8849469321
  • Previous prime number is 7

Basic properties

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