Replace <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mn>90</mn><mo>-</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> with an equivalent expression <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mn>90</mn><mo>-</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> using the fundamental identities.

Use the difference formula for sine to simplify the expression. The formula states that <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>-</mo><mi>B</mi><mo>)</mo></mrow><mo>=</mo><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>-</mo><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mstyle></math> .

Remove parentheses.

Simplify each term.

The exact value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>90</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>90</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Convert from <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> to <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Do you know how to Expand Using Sum/Difference Formulas csc(90-theta)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | two billion five million seven hundred seventy-eight thousand seven hundred sixty-eight |
---|

- 2005778768 has 64 divisors, whose sum is
**10185145740** - The reverse of 2005778768 is
**8678775002** - Previous prime number is
**329**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 50
- Digital Root 5

Name | two hundred forty million one hundred seventy thousand three hundred thirty-six |
---|

- 240170336 has 256 divisors, whose sum is
**2194076160** - The reverse of 240170336 is
**633071042** - Previous prime number is
**19**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 26
- Digital Root 8

Name | one billion three hundred forty-five million five hundred forty-two thousand one hundred four |
---|

- 1345542104 has 32 divisors, whose sum is
**4687695936** - The reverse of 1345542104 is
**4012455431** - Previous prime number is
**31**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 29
- Digital Root 2