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 | one billion six hundred sixty-seven million five hundred eighty-seven thousand five hundred sixty-five |
---|

- 1667587565 has 8 divisors, whose sum is
**1717023744** - The reverse of 1667587565 is
**5657857661** - Previous prime number is
**977**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 56
- Digital Root 2

Name | nine hundred ten million three hundred six thousand three hundred eighty-six |
---|

- 910306386 has 32 divisors, whose sum is
**1657791360** - The reverse of 910306386 is
**683603019** - Previous prime number is
**677**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 36
- Digital Root 9

Name | one billion four hundred ninety-one million three hundred thirty-seven thousand eight hundred thirty-three |
---|

- 1491337833 has 8 divisors, whose sum is
**1988938848** - The reverse of 1491337833 is
**3387331941** - Previous prime number is
**4217**

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