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 | one billion four hundred fifty-three million four hundred six thousand two hundred eighty-three |
---|

- 1453406283 has 8 divisors, whose sum is
**1481534208** - The reverse of 1453406283 is
**3826043541** - Previous prime number is
**293**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 36
- Digital Root 9

Name | three hundred fifty-eight million two hundred twelve thousand six hundred forty-two |
---|

- 358212642 has 16 divisors, whose sum is
**719282592** - The reverse of 358212642 is
**246212853** - Previous prime number is
**251**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 33
- Digital Root 6

Name | one hundred eighty-one million four hundred seventy thousand eight hundred seventy-three |
---|

- 181470873 has 4 divisors, whose sum is
**241961168** - The reverse of 181470873 is
**378074181** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 39
- Digital Root 3