Verify the Identity csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2

Verify the Identity csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2
Start on the right side.
Factor out of .
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Factor out of .
Multiply by .
Factor out of .
Apply Pythagorean identity.
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Rearrange terms.
Apply pythagorean identity.
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
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One to any power is one.
One to any power is one.
Apply the distributive property.
Multiply .
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Multiply and .
Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Add and .
Rewrite as .
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.
Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Add and .
Combine the numerators over the common denominator.
Simplify the numerator.
Now consider the left side of the equation.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
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Simplify each term.
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One to any power is one.
One to any power is one.
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.
Multiply by by adding the exponents.
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Use the power rule to combine exponents.
Add and .
Combine the numerators over the common denominator.
Simplify the numerator.
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 two hundred forty-three million four hundred two thousand one hundred twenty-five

Interesting facts

  • 1243402125 has 16 divisors, whose sum is 1341756416
  • The reverse of 1243402125 is 5212043421
  • Previous prime number is 181

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 24
  • Digital Root 6

Name

Name one billion nine hundred sixty-eight million eight hundred thirteen thousand two hundred thirty-five

Interesting facts

  • 1968813235 has 4 divisors, whose sum is 1978417408
  • The reverse of 1968813235 is 5323188691
  • Previous prime number is 205

Basic properties

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

Name

Name one billion eight hundred sixty-three million eight hundred seventy-four thousand nine hundred twenty-eight

Interesting facts

  • 1863874928 has 32 divisors, whose sum is 9435866904
  • The reverse of 1863874928 is 8294783681
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 56
  • Digital Root 2