# Verify the Identity (1-cos(x))/(sin(x))+(sin(x))/(1-cos(x))=2csc(x)

Verify the Identity (1-cos(x))/(sin(x))+(sin(x))/(1-cos(x))=2csc(x)
Start on the left 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 .
Combine.
Combine.
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify each term.
Simplify denominator.
Apply the distributive property.
Multiply by .
Simplify each term.
Apply pythagorean identity.
Simplify.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Factor out of .
Factor out of .
Cancel the common factor of .
Now consider the right side of the equation.
Apply the reciprocal identity to .
Combine and .
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 four hundred sixty-seven million four hundred forty-two thousand five hundred seventy-three

### Interesting facts

• 1467442573 has 16 divisors, whose sum is 1554973056
• The reverse of 1467442573 is 3752447641
• Previous prime number is 83

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 43
• Digital Root 7

### Name

Name one billion three hundred fifty-two million three hundred fifty-eight thousand eight hundred seventy-two

### Interesting facts

• 1352358872 has 32 divisors, whose sum is 4626736632
• The reverse of 1352358872 is 2788532531
• Previous prime number is 73

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 44
• Digital Root 8

### Name

Name nine hundred forty-eight million four hundred forty-three thousand six hundred ninety-four

### Interesting facts

• 948443694 has 8 divisors, whose sum is 1465776720
• The reverse of 948443694 is 496344849
• Previous prime number is 33

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 51
• Digital Root 6