Start on the left side.

Apply pythagorean identity.

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

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

Apply pythagorean 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> .

One to any power is one.

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

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><msup><mi>sin</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><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"><mo>-</mo><msup><mi>tan</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</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(x)^2+1)(cos(x)^2-1)=-tan(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 | five hundred ninety-six million nine hundred thirty-eight thousand two hundred fifty-four |
---|

- 596938254 has 32 divisors, whose sum is
**1420813440** - The reverse of 596938254 is
**452839695** - Previous prime number is
**11**

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

Name | seven hundred fifty million four hundred sixty-eight thousand one hundred thirteen |
---|

- 750468113 has 4 divisors, whose sum is
**750549360** - The reverse of 750468113 is
**311864057** - Previous prime number is
**10627**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 35
- Digital Root 8

Name | one billion nine hundred fifty-three million five hundred three thousand five hundred eighteen |
---|

- 1953503518 has 4 divisors, whose sum is
**2930255280** - The reverse of 1953503518 is
**8153053591** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 40
- Digital Root 4