# 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 .
Factor out of .
Multiply by .
Factor out of .
Apply Pythagorean identity.
Rearrange terms.
Apply pythagorean identity.
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
One to any power is one.
One to any power is one.
Apply the distributive property.
Multiply .
Multiply and .
Multiply by by adding the exponents.
Use the power rule to combine exponents.
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 .
Combine.
Multiply by by adding the exponents.
Use the power rule to combine exponents.
Combine the numerators over the common denominator.
Simplify the numerator.
Now consider the left side of the equation.
Convert to sines and cosines.
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
Simplify each term.
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 .
Combine.
Multiply by by adding the exponents.
Use the power rule to combine exponents.
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