Start on the left side.

Since <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> is an odd function, rewrite <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Since <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> is an even function, rewrite <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mo>-</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply the reciprocal identity to <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply the reciprocal identity to <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Multiply the numerator by the reciprocal of the denominator.

Combine <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Write <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> as a fraction with denominator <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

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

Move the negative in front of the fraction.

Now consider the right side of the equation.

Write <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> in sines and cosines using the quotient identity.

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

Do you know how to Verify the Identity (csc(-x))/(sec(-x))=-cot(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 | four hundred fourteen million three hundred ninety-seven thousand sixty-eight |
---|

- 414397068 has 32 divisors, whose sum is
**950223744** - The reverse of 414397068 is
**860793414** - Previous prime number is
**997**

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

Name | one billion ninety-seven million one hundred twenty-eight thousand three hundred seventy-eight |
---|

- 1097128378 has 16 divisors, whose sum is
**1699729920** - The reverse of 1097128378 is
**8738217901** - Previous prime number is
**2341**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | three hundred forty-three million seven hundred seventy-five thousand five hundred ninety-six |
---|

- 343775596 has 16 divisors, whose sum is
**788089824** - The reverse of 343775596 is
**695577343** - Previous prime number is
**53**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 49
- Digital Root 4