# Verify the Identity (csc(-x))/(sec(-x))=-cot(x)

Verify the Identity (csc(-x))/(sec(-x))=-cot(x)
Start on the left side.
Since is an odd function, rewrite as .
Since is an even function, rewrite as .
Convert to sines and cosines.
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Simplify.
Multiply the numerator by the reciprocal of the denominator.
Combine and .
Write as a fraction with denominator .
Combine.
Multiply by .
Move the negative in front of the fraction.
Now consider the right side of the equation.
Write in sines and cosines using the quotient identity.
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 fourteen million three hundred ninety-seven thousand sixty-eight

### Interesting facts

• 414397068 has 32 divisors, whose sum is 950223744
• The reverse of 414397068 is 860793414
• Previous prime number is 997

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 42
• Digital Root 6

### Name

Name one billion ninety-seven million one hundred twenty-eight thousand three hundred seventy-eight

### Interesting facts

• 1097128378 has 16 divisors, whose sum is 1699729920
• The reverse of 1097128378 is 8738217901
• Previous prime number is 2341

### Basic properties

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

### Name

Name three hundred forty-three million seven hundred seventy-five thousand five hundred ninety-six

### Interesting facts

• 343775596 has 16 divisors, whose sum is 788089824
• The reverse of 343775596 is 695577343
• Previous prime number is 53

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 49
• Digital Root 4