Start on the right side.

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

Apply Pythagorean identity in reverse.

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

Simplify each term.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><msup><mrow><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> and <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Cancel the common factors.

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

Cancel the common factor.

Rewrite the expression.

Combine the numerators over the common denominator.

Subtract <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mstyle></math> from <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mstyle></math> .

Add <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></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 tan(A)=tan(A)*csc(A)^2+cot(-A)? 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 nine million seventeen thousand eight hundred sixty-eight |
---|

- 209017868 has 32 divisors, whose sum is
**476358624** - The reverse of 209017868 is
**868710902** - Previous prime number is
**167**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 41
- Digital Root 5

Name | two billion one hundred thirty-three million nine hundred seventy-seven thousand six hundred |
---|

- 2133977600 has 8192 divisors, whose sum is
**118745177040** - The reverse of 2133977600 is
**0067793312** - Previous prime number is
**293**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 38
- Digital Root 2

Name | one billion six hundred forty-nine million seven hundred thirty-two thousand three hundred twenty |
---|

- 1649732320 has 128 divisors, whose sum is
**12595417056** - The reverse of 1649732320 is
**0232379461** - Previous prime number is
**185**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 37
- Digital Root 1