Start on the left side.

Apply Pythagorean identity in reverse.

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 reciprocal identity to <math><mstyle displaystyle="true"><mi>sec</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>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Multiply the numerator by the reciprocal of the denominator.

One to any power is one.

Simplify the denominator.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

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

To write <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Combine.

Multiply <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> .

Combine <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn><mo>+</mo><mn>2</mn><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> .

Reduce the expression <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>+</mo><mn>2</mn><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow><mrow><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> by cancelling the common factors.

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

Cancel the common factor.

Rewrite the expression.

Multiply the numerator by the reciprocal of the denominator.

Combine <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mo>-</mo><mn>1</mn><mo>+</mo><mn>2</mn><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mn>2</mn><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

Write <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> as a fraction with denominator <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Remove parentheses.

Multiply <math><mstyle displaystyle="true"><mn>1</mn><mo>-</mo><mn>2</mn><msup><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Move the negative in front of the fraction.

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>-</mo><mn>2</mn><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></mrow></mfrac></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(x))/(1-tan(x)^2)=(sin(x)cos(x))/(2cos(x)^2-1)? 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 | one billion nine hundred twenty-five million eight hundred eighty-two thousand three hundred forty-six |
---|

- 1925882346 has 16 divisors, whose sum is
**3853665504** - The reverse of 1925882346 is
**6432885291** - Previous prime number is
**2053**

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

Name | one billion five hundred ninety-three million seven hundred forty-seven thousand four hundred twenty-four |
---|

- 1593747424 has 128 divisors, whose sum is
**12213578520** - The reverse of 1593747424 is
**4247473951** - Previous prime number is
**109**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | one hundred fifty-eight million seven hundred seventy-five thousand two hundred two |
---|

- 158775202 has 8 divisors, whose sum is
**238289436** - The reverse of 158775202 is
**202577851** - Previous prime number is
**1973**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 37
- Digital Root 1