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 one billion seventy-two million nine hundred five thousand seventy-five

Interesting facts

  • 1072905075 has 16 divisors, whose sum is 1179160320
  • The reverse of 1072905075 is 5705092701
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 36
  • Digital Root 9

Name

Name eight hundred ninety-seven million eight hundred forty-three thousand seventy-five

Interesting facts

  • 897843075 has 16 divisors, whose sum is 1723858848
  • The reverse of 897843075 is 570348798
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 51
  • Digital Root 6

Name

Name one billion six hundred twenty-six million four hundred thirty-two thousand three hundred fifteen

Interesting facts

  • 1626432315 has 8 divisors, whose sum is 1751706112
  • The reverse of 1626432315 is 5132346261
  • Previous prime number is 103

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 33
  • Digital Root 6