# 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.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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