Verify the Identity 1/(1-sin(x))+1/(1+sin(x))=2sec(x)^2

Verify the Identity 1/(1-sin(x))+1/(1+sin(x))=2sec(x)^2
Start on the left side.
Add fractions.
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To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Combine.
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify numerator.
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Simplify each term.
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Multiply by .
Multiply by .
Add and .
Subtract from .
Add and .
Simplify denominator.
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Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Apply pythagorean identity.
Now consider the right side of the equation.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the product rule to .
Simplify.
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One to any power is one.
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 six hundred eighty-nine million six hundred fifty-seven thousand four hundred eighty-four

Interesting facts

  • 689657484 has 16 divisors, whose sum is 1574218800
  • The reverse of 689657484 is 484756986
  • Previous prime number is 69

Basic properties

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

Name

Name seven hundred seventy million three hundred two thousand six hundred seventy-two

Interesting facts

  • 770302672 has 64 divisors, whose sum is 3905737056
  • The reverse of 770302672 is 276203077
  • Previous prime number is 647

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 34
  • Digital Root 7

Name

Name one hundred eighty-two million eight hundred fifty-one thousand five hundred ninety-five

Interesting facts

  • 182851595 has 4 divisors, whose sum is 182883288
  • The reverse of 182851595 is 595158281
  • Previous prime number is 7585

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 44
  • Digital Root 8