# 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 eight hundred seven million eight hundred thirty-seven thousand nine hundred twenty-nine

### Interesting facts

• 1807837929 has 8 divisors, whose sum is 2009392000
• The reverse of 1807837929 is 9297387081
• Previous prime number is 3079

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 54
• Digital Root 9

### Name

Name three hundred seventy-eight million eight hundred eighty-six thousand nine hundred eighty

### Interesting facts

• 378886980 has 64 divisors, whose sum is 963532800
• The reverse of 378886980 is 089688873
• Previous prime number is 19

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 57
• Digital Root 3

### Name

Name one billion six hundred ninety-eight million five hundred eighty-six thousand eight hundred ninety-five

### Interesting facts

• 1698586895 has 4 divisors, whose sum is 2038304280
• The reverse of 1698586895 is 5986858961
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 65
• Digital Root 2