Start on the left side.

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

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.

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.

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

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> into the numerator.

Factor <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mi>sin</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>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

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

Do you know how to Verify the Identity tan(-x)cot(x)=-1? 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 | seven hundred eighty million six hundred ninety-five thousand two hundred fifty-nine |
---|

- 780695259 has 4 divisors, whose sum is
**1040927016** - The reverse of 780695259 is
**952596087** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 51
- Digital Root 6

Name | one billion two hundred sixty-seven million nine hundred thirty-nine thousand two hundred eighty-three |
---|

- 1267939283 has 8 divisors, whose sum is
**1379551488** - The reverse of 1267939283 is
**3829397621** - Previous prime number is
**97**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 50
- Digital Root 5

Name | seven hundred thirty-nine million three hundred seventy-four thousand one hundred forty-six |
---|

- 739374146 has 32 divisors, whose sum is
**1324919808** - The reverse of 739374146 is
**641473937** - Previous prime number is
**691**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 44
- Digital Root 8