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 | two hundred seventy-one million three hundred twenty-seven thousand one hundred eighteen |
---|

- 271327118 has 8 divisors, whose sum is
**410195712** - The reverse of 271327118 is
**811723172** - Previous prime number is
**127**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | one billion seven hundred eleven million four hundred thirty-eight thousand three hundred thirteen |
---|

- 1711438313 has 16 divisors, whose sum is
**1888641216** - The reverse of 1711438313 is
**3138341171** - Previous prime number is
**43**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 32
- Digital Root 5

Name | one billion twenty-five million three thousand thirty-nine |
---|

- 1025003039 has 4 divisors, whose sum is
**1025101056** - The reverse of 1025003039 is
**9303005201** - Previous prime number is
**11903**

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