Start on the left side.

Simplify each term.

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

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

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></mfrac><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

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

Rewrite using the commutative property of multiplication.

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

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

Rewrite using the commutative property of multiplication.

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

Combine <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>B</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>B</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> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Add <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</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>B</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>B</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>B</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>B</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><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 (sec(B)+tan(B))(1-sin(B))=cos(B)? 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 fifty-eight million nine hundred sixty-seven thousand eight hundred twenty-three |
---|

- 1658967823 has 4 divisors, whose sum is
**1716173640** - The reverse of 1658967823 is
**3287698561** - Previous prime number is
**29**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 55
- Digital Root 1

Name | one billion eight hundred forty-nine million eight hundred seventy-eight thousand ninety-two |
---|

- 1849878092 has 8 divisors, whose sum is
**4162225716** - The reverse of 1849878092 is
**2908789481** - Previous prime number is
**2**

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

Name | one billion one hundred fifty-four million fifty-four thousand one hundred forty-six |
---|

- 1154054146 has 32 divisors, whose sum is
**2096658432** - The reverse of 1154054146 is
**6414504511** - Previous prime number is
**2297**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 31
- Digital Root 4