Split <math><mstyle displaystyle="true"><mn>105</mn></mstyle></math> into two angles where the values of the six trigonometric functions are known.

Apply the sum of angles identity.

The exact value of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>45</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>60</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>45</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>60</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> .

Simplify the denominator.

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

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><msqrt><mn>3</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><msqrt><mn>3</mn></msqrt></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>1</mn><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>1</mn><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> .

Expand the denominator using the FOIL method.

Simplify.

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></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> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><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"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine using the product rule for radicals.

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><msqrt><mn>3</mn></msqrt></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mrow><mo>(</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Move the negative one from the denominator of <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mo>⋅</mo><mrow><mo>(</mo><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mrow><mo>(</mo><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow></mstyle></math> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Do you know how to Find the Exact Value tan(105)? 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 | three hundred thirty-three million one hundred seventy-nine thousand two hundred fifty-three |
---|

- 333179253 has 16 divisors, whose sum is
**411480000** - The reverse of 333179253 is
**352971333** - Previous prime number is
**53**

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

Name | seven hundred fifty-three million four hundred seventy-three thousand nine hundred sixty-eight |
---|

- 753473968 has 128 divisors, whose sum is
**4125201696** - The reverse of 753473968 is
**869374357** - Previous prime number is
**241**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 52
- Digital Root 7

Name | two hundred twenty-six million nine hundred eighty-six thousand nine hundred seventy-two |
---|

- 226986972 has 16 divisors, whose sum is
**680960952** - The reverse of 226986972 is
**279689622** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 51
- Digital Root 6