Start on the left side.

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

Write <math><mstyle displaystyle="true"><mo>-</mo><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> as a fraction with denominator <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

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

Combine the numerators over the common denominator.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply pythagorean identity.

Now consider the right side of the equation.

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.

Multiply <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></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 sec(x)-cos(x)=sin(x)tan(x)? 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 billion eighty-five million six hundred twenty-five thousand one hundred thirty-eight |
---|

- 2085625138 has 8 divisors, whose sum is
**3128961132** - The reverse of 2085625138 is
**8315265802** - Previous prime number is
**6197**

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

Name | one billion seven hundred thirty-four million eight hundred seventy-five thousand nine hundred eighty-five |
---|

- 1734875985 has 8 divisors, whose sum is
**1889908224** - The reverse of 1734875985 is
**5895784371** - Previous prime number is
**47**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 57
- Digital Root 3

Name | six hundred fifty-three million four hundred fifty-nine thousand seven hundred forty-seven |
---|

- 653459747 has 4 divisors, whose sum is
**661332840** - The reverse of 653459747 is
**747954356** - Previous prime number is
**83**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 50
- Digital Root 5