# 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 eight hundred fifty-seven million five hundred twelve thousand eighty-nine

### Interesting facts

• 1857512089 has 16 divisors, whose sum is 2040923520
• The reverse of 1857512089 is 9802157581
• Previous prime number is 331

### Basic properties

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

### Name

Name one billion three hundred ninety-five million two hundred seventy-one thousand fifty

### Interesting facts

• 1395271050 has 32 divisors, whose sum is 4018381056
• The reverse of 1395271050 is 0501725931
• Previous prime number is 5

### Basic properties

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

### Name

Name two hundred twenty-five million two hundred forty-four thousand one hundred seventy-one

### Interesting facts

• 225244171 has 8 divisors, whose sum is 233532800
• The reverse of 225244171 is 171442522
• Previous prime number is 229

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 28
• Digital Root 1