# 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 four hundred ninety-nine million five hundred twenty-seven thousand two hundred forty-five

### Interesting facts

• 499527245 has 32 divisors, whose sum is 699217920
• The reverse of 499527245 is 542725994
• Previous prime number is 179

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 47
• Digital Root 2

### Name

Name five hundred seventy-four million four hundred twenty-six thousand four hundred thirty-two

### Interesting facts

• 574426432 has 512 divisors, whose sum is 6811630200
• The reverse of 574426432 is 234624475
• Previous prime number is 173

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 37
• Digital Root 1

### Name

Name one billion five hundred nine million five hundred eleven thousand three hundred forty-six

### Interesting facts

• 1509511346 has 16 divisors, whose sum is 2957410176
• The reverse of 1509511346 is 6431159051
• Previous prime number is 7

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 35
• Digital Root 8