Verify the Identity cos(x-pi/4)=( square root of 2)/2(cos(x)+sin(x))

Verify the Identity cos(x-pi/4)=( square root of 2)/2(cos(x)+sin(x))
Start on the left side.
Apply the difference of angles identity .
Simplify each term.
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The exact value of is .
Combine and .
The exact value of is .
Combine and .
Reorder factors in .
Now consider the right side of the equation.
Simplify.
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Apply the distributive property.
Combine and .
Combine and .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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Name

Name thirty-one million six hundred thirty-four thousand four hundred three

Interesting facts

  • 31634403 has 4 divisors, whose sum is 42179208
  • The reverse of 31634403 is 30443613
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 8
  • Sum of Digits 24
  • Digital Root 6

Name

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

Interesting facts

  • 1397895040 has 1024 divisors, whose sum is 30347406864
  • The reverse of 1397895040 is 0405987931
  • Previous prime number is 17

Basic properties

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

Name

Name one hundred sixty-five million nine hundred sixty thousand six hundred twenty-four

Interesting facts

  • 165960624 has 64 divisors, whose sum is 1120234536
  • The reverse of 165960624 is 426069561
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3