# Verify the Identity cot(x)(cot(x)+tan(x))=csc(x)^2

Verify the Identity cot(x)(cot(x)+tan(x))=csc(x)^2
Start on the left side.
Apply the distributive property.
Multiply .
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
Apply the reciprocal identity to .
Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Apply the product rule to .
Simplify.
Simplify each term.
One to any power is one.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Now consider the right side of the equation.
Convert to sines and cosines.
Apply the reciprocal identity to .
Apply the product rule to .
One to any power is one.
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 one hundred seventy million one hundred eleven thousand five hundred sixty-one

### Interesting facts

• 1170111561 has 16 divisors, whose sum is 1645443840
• The reverse of 1170111561 is 1651110711
• Previous prime number is 523

### Basic properties

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

### Name

Name two billion one hundred twenty-six million two hundred twenty-eight thousand ninety

### Interesting facts

• 2126228090 has 32 divisors, whose sum is 4040010000
• The reverse of 2126228090 is 0908226212
• Previous prime number is 29

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 32
• Digital Root 5

### Name

Name one billion one hundred forty-two million fifty-nine thousand two hundred twenty-two

### Interesting facts

• 1142059222 has 8 divisors, whose sum is 1713616776
• The reverse of 1142059222 is 2229502411
• Previous prime number is 3307

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 28
• Digital Root 1