Expand Using Sum/Difference Formulas csc(pi/2-x)

$\csc (\frac{π}{2} - x)$

Replace $\csc (\frac{π}{2} - x)$ with an equivalent expression $\frac{1}{\sin (\frac{π}{2} - x)}$ using the fundamental identities.

$\frac{1}{\sin (\frac{π}{2} - x)}$

Use a sum or difference formula on the denominator.

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Use the difference formula for sine to simplify the expression. The formula states that $\sin (A - B) = \sin (A) \cos (B) - \cos (A) \sin (B)$ .

$\frac{1}{\sin (\frac{π}{2}) \cos (x) - \cos (\frac{π}{2}) \sin (x)}$

Remove parentheses.

$\frac{1}{\sin (\frac{π}{2}) \cos (x) - \cos (\frac{π}{2}) \sin (x)}$

Simplify each term.

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The exact value of $\sin (\frac{π}{2})$ is $1$ .

$\frac{1}{1 \cos (x) - \cos (\frac{π}{2}) \sin (x)}$

Multiply $\cos (x)$ by $1$ .

$\frac{1}{\cos (x) - \cos (\frac{π}{2}) \sin (x)}$

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$\frac{1}{\cos (x) + 0 \sin (x)}$

Multiply $- 1$ by $0$ .

$\frac{1}{\cos (x) + 0 \sin (x)}$

Multiply $0$ by $\sin (x)$ .

$\frac{1}{\cos (x) + 0}$

Add $\cos (x)$ and $0$ .

$\frac{1}{\cos (x)}$

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\sec (x)$

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Name

Name	one billion two hundred forty-eight million five hundred fifty-four thousand forty-seven

Interesting facts

1248554047 has 16 divisors, whose sum is 1411522560
The reverse of 1248554047 is 7404558421
Previous prime number is 59

Basic properties

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

Name

Name	three hundred seventy-one million six hundred ninety-five thousand nine hundred thirty-seven

Interesting facts

371695937 has 4 divisors, whose sum is 372499200
The reverse of 371695937 is 739596173
Previous prime number is 463

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 50
Digital Root 5

Name

Name	two billion eight million one hundred seventy-six thousand six hundred ninety-eight

Interesting facts

2008176698 has 16 divisors, whose sum is 3292409376
The reverse of 2008176698 is 8966718002
Previous prime number is 523

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 47
Digital Root 2

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