Simplify terms.

Simplify each term.

Rewrite <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> in terms of sines and cosines.

Rewrite <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> in terms of sines and cosines.

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

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>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> .

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

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

Combine the numerators over the common denominator.

Apply pythagorean identity.

Cancel the common factor 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> and <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

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><mi>cos</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Cancel the common factors.

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

Cancel the common factor.

Rewrite the expression.

Divide <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> .

Rewrite <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> in terms of sines and cosines.

Multiply by the reciprocal of the fraction to divide by <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 <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> .

For the two functions to be equal, the arguments of each must be equal.

Subtract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Since <math><mstyle displaystyle="true"><mn>0</mn><mo>=</mo><mn>0</mn></mstyle></math> , the equation will always be true.

Always true

Do you know how to Verify sec(x)-tan(x)sin(x)=1/(sec(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 | forty-two million one hundred ninety-six thousand five hundred eighty-four |
---|

- 42196584 has 64 divisors, whose sum is
**201056256** - The reverse of 42196584 is
**48569124** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 8
- Sum of Digits 39
- Digital Root 3

Name | sixty-five million nine hundred forty-eight thousand four hundred twenty-one |
---|

- 65948421 has 32 divisors, whose sum is
**111200256** - The reverse of 65948421 is
**12484956** - Previous prime number is
**71**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 39
- Digital Root 3

Name | one billion seven hundred sixteen million three hundred nine thousand one hundred fifteen |
---|

- 1716309115 has 16 divisors, whose sum is
**2097538560** - The reverse of 1716309115 is
**5119036171** - Previous prime number is
**7747**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 34
- Digital Root 7