# Verify the Identity 2cot(x)csc(x)=1/(sec(x)-1)+1/(sec(x)+1)

Verify the Identity 2cot(x)csc(x)=1/(sec(x)-1)+1/(sec(x)+1)
Start on the right side.
To write as a fraction with a common denominator, multiply by .
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 .
Multiply and .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify numerator.
Subtract from .
Simplify denominator.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Apply pythagorean identity.
Convert to sines and cosines.
Apply the reciprocal identity to .
Write in sines and cosines using the quotient identity.
Apply the product rule to .
Simplify.
Multiply the numerator by the reciprocal of the denominator.
Combine and .
Combine.
Cancel the common factor of and .
Rewrite as .
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 five million seven hundred fifty-one thousand five hundred ninety-seven

### Interesting facts

• 1005751597 has 4 divisors, whose sum is 1012987360
• The reverse of 1005751597 is 7951575001
• Previous prime number is 139

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 40
• Digital Root 4

### Name

Name nine hundred seventeen million two hundred sixty-three thousand seven hundred twenty-three

### Interesting facts

• 917263723 has 4 divisors, whose sum is 924486400
• The reverse of 917263723 is 327362719
• Previous prime number is 127

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 40
• Digital Root 4

### Name

Name one billion one hundred eighty-nine million three hundred eighteen thousand nine hundred fifteen

### Interesting facts

• 1189318915 has 8 divisors, whose sum is 1429072560
• The reverse of 1189318915 is 5198139811
• Previous prime number is 757

### Basic properties

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