Start on the left side.

Apply pythagorean identity.

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

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

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Multiply the numerator by the reciprocal of the denominator.

Combine.

Cancel the common factor of <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

One to any power is one.

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></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 (csc(theta)^2)/(csc(theta)^2-1)=sec(theta)^2? 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 | three hundred ninety-six million eight hundred nineteen thousand nine |
---|

- 396819009 has 8 divisors, whose sum is
**464116000** - The reverse of 396819009 is
**900918693** - Previous prime number is
**19**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 45
- Digital Root 9

Name | one hundred seven million three hundred nine thousand four hundred fifty |
---|

- 107309450 has 32 divisors, whose sum is
**232104960** - The reverse of 107309450 is
**054903701** - Previous prime number is
**1471**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 29
- Digital Root 2

Name | nine hundred ten million nine hundred twenty-three thousand eight hundred thirty |
---|

- 910923830 has 8 divisors, whose sum is
**1639662912** - The reverse of 910923830 is
**038329019** - Previous prime number is
**5**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 35
- Digital Root 8