Start on the left side.

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.

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

To write <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> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</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> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <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> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</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> .

Reorder the factors of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Combine the numerators over the common denominator.

Simplify each term.

Rearrange terms.

Apply pythagorean identity.

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><mi>csc</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</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 cot(theta)+tan(theta)=(csc(theta))/(cos(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 one hundred ninety-five million one hundred sixty-two thousand six hundred forty-eight |
---|

- 1195162648 has 16 divisors, whose sum is
**4033673964** - The reverse of 1195162648 is
**8462615911** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | one billion five hundred forty-six million nine hundred thirty-six thousand six hundred thirty-one |
---|

- 1546936631 has 4 divisors, whose sum is
**1548849600** - The reverse of 1546936631 is
**1366396451** - Previous prime number is
**809**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 44
- Digital Root 8

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

- 1008204341 has 4 divisors, whose sum is
**1008270252** - The reverse of 1008204341 is
**1434028001** - Previous prime number is
**41777**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 23
- Digital Root 5