Start on the left side.

Separate fractions.

Rewrite <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> in terms of sines and cosines.

Multiply by the reciprocal of the fraction to divide by <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Write <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as a fraction with denominator <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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.

Divide <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

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

Apply Pythagorean identity in reverse.

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

Do you know how to Verify the Identity (cos(x)sin(x))/(cot(x))=1-cos(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 hundred thirty-seven million five hundred fifty-six thousand nine hundred seventy-eight |
---|

- 137556978 has 16 divisors, whose sum is
**296276736** - The reverse of 137556978 is
**879655731** - Previous prime number is
**13**

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

Name | one billion five hundred sixty-one million one hundred fifteen thousand one hundred ten |
---|

- 1561115110 has 16 divisors, whose sum is
**2932181856** - The reverse of 1561115110 is
**0115111651** - Previous prime number is
**23**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 22
- Digital Root 4

Name | one billion eight hundred sixty-four million seven hundred thirty-eight thousand six hundred forty |
---|

- 1864738640 has 128 divisors, whose sum is
**11497399200** - The reverse of 1864738640 is
**0468374681** - Previous prime number is
**67**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 47
- Digital Root 2