# Verify the Identity (csc(theta)^2)/(csc(theta)^2-1)=sec(theta)^2

Verify the Identity (csc(theta)^2)/(csc(theta)^2-1)=sec(theta)^2
Start on the left side.
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 .
Apply the product rule to .
Simplify.
Multiply the numerator by the reciprocal of the denominator.
Combine.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
One to any power is one.
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 three hundred ninety-six million eight hundred nineteen thousand nine

### Interesting facts

• 396819009 has 8 divisors, whose sum is 464116000
• The reverse of 396819009 is 900918693
• Previous prime number is 19

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 45
• Digital Root 9

### Name

Name one hundred seven million three hundred nine thousand four hundred fifty

### Interesting facts

• 107309450 has 32 divisors, whose sum is 232104960
• The reverse of 107309450 is 054903701
• Previous prime number is 1471

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 29
• Digital Root 2

### Name

Name nine hundred ten million nine hundred twenty-three thousand eight hundred thirty

### Interesting facts

• 910923830 has 8 divisors, whose sum is 1639662912
• The reverse of 910923830 is 038329019
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 35
• Digital Root 8