Start on the left side.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>cot</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply Pythagorean identity in reverse.

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

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.

Write <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</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>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Simplify each term.

One to any power is one.

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

Cancel the common factor.

Rewrite the expression.

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

Cancel the common factor.

Rewrite the expression.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Now consider the right side of the equation.

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 product rule to <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> .

One to any power is one.

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

Do you know how to Verify the Identity cot(x)(cot(x)+tan(x))=csc(x)^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 | one billion one hundred seventy million one hundred eleven thousand five hundred sixty-one |
---|

- 1170111561 has 16 divisors, whose sum is
**1645443840** - The reverse of 1170111561 is
**1651110711** - Previous prime number is
**523**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 24
- Digital Root 6

Name | two billion one hundred twenty-six million two hundred twenty-eight thousand ninety |
---|

- 2126228090 has 32 divisors, whose sum is
**4040010000** - The reverse of 2126228090 is
**0908226212** - Previous prime number is
**29**

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

Name | one billion one hundred forty-two million fifty-nine thousand two hundred twenty-two |
---|

- 1142059222 has 8 divisors, whose sum is
**1713616776** - The reverse of 1142059222 is
**2229502411** - Previous prime number is
**3307**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 28
- Digital Root 1