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 | one billion four hundred sixteen million eight hundred thirty-five thousand seven hundred eighty-five |
---|

- 1416835785 has 16 divisors, whose sum is
**2282155200** - The reverse of 1416835785 is
**5875386141** - Previous prime number is
**149**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 48
- Digital Root 3

Name | one hundred thirty million eight hundred ten thousand three hundred fifty-five |
---|

- 130810355 has 16 divisors, whose sum is
**159060000** - The reverse of 130810355 is
**553018031** - Previous prime number is
**499**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 26
- Digital Root 8

Name | six hundred seventy-six million seven hundred thirty-six thousand eight hundred eighty-six |
---|

- 676736886 has 32 divisors, whose sum is
**1560526848** - The reverse of 676736886 is
**688637676** - Previous prime number is
**113**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 57
- Digital Root 3