Start on the left side.

Apply Pythagorean identity in reverse.

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

One to any power is one.

Apply the distributive property.

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

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

Reorder terms.

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> as <math><mstyle displaystyle="true"><msup><mi>sec</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></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 sin(theta)^2sec(theta)^2=sec(theta)^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 two hundred fifty-five million nine hundred thirty-two thousand eight hundred twenty-five |
---|

- 1255932825 has 32 divisors, whose sum is
**1605132288** - The reverse of 1255932825 is
**5282395521** - Previous prime number is
**7**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 42
- Digital Root 6

Name | one billion two hundred fifty-four million nine hundred fifty-six thousand three hundred seventy-three |
---|

- 1254956373 has 16 divisors, whose sum is
**1546948800** - The reverse of 1254956373 is
**3736594521** - Previous prime number is
**59**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 45
- Digital Root 9

Name | eight hundred forty-nine million three hundred seventy-seven thousand nine hundred one |
---|

- 849377901 has 16 divisors, whose sum is
**1148130560** - The reverse of 849377901 is
**109773948** - Previous prime number is
**1321**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 48
- Digital Root 3