Start on the left side.

Apply Pythagorean identity in reverse.

Simplify the numerator.

Rewrite <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Since both terms are perfect squares, factor using the difference of squares formula, <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> where <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>1</mn><mo>+</mo><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1</mn><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><mn>1</mn><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Because the two sides have been shown to be equivalent, the equation is an identity.

Do you know how to Verify the Identity (cos(x)^2)/(1+sin(x))=1-1/(csc(x))? 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 hundred eighty-five million six hundred thirty-two thousand seven hundred eighty-one |
---|

- 185632781 has 4 divisors, whose sum is
**185779200** - The reverse of 185632781 is
**187236581** - Previous prime number is
**1279**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 41
- Digital Root 5

Name | one billion six hundred seventy-two million three hundred fifty-four thousand sixty-two |
---|

- 1672354062 has 8 divisors, whose sum is
**2787256800** - The reverse of 1672354062 is
**2604532761** - Previous prime number is
**9**

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

Name | four hundred sixteen million nine hundred thirty thousand seven hundred thirty-nine |
---|

- 416930739 has 4 divisors, whose sum is
**555907656** - The reverse of 416930739 is
**937039614** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 42
- Digital Root 6