Rewrite <math><mstyle displaystyle="true"><mn>112.5</mn></mstyle></math> as an angle where the values of the six trigonometric functions are known divided by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Apply the tangent half-angle identity.

Change the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo></mstyle></math> because tangent is negative in the second quadrant.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>45</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mo>-</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

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

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>2</mn></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"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

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

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>45</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>2</mn></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"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

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

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mo>-</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac></mstyle></math> .

Expand the denominator using the FOIL method.

Simplify.

Apply the distributive property.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Simplify each term.

Apply the distributive property.

Move <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> .

Combine using the product rule for radicals.

Simplify each term.

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

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

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

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

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

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><msqrt><mn>2</mn></msqrt><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Cancel the common factors.

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

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Do you know how to Find the Exact Value tan(112.5)? 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 | eight hundred ten million three hundred thirty-two thousand nine hundred seventy-seven |
---|

- 810332977 has 8 divisors, whose sum is
**813512000** - The reverse of 810332977 is
**779233018** - Previous prime number is
**1399**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 40
- Digital Root 4

Name | one billion thirty-two million nine hundred sixty-four thousand three hundred forty-four |
---|

- 1032964344 has 64 divisors, whose sum is
**3903221520** - The reverse of 1032964344 is
**4434692301** - Previous prime number is
**131**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 36
- Digital Root 9

Name | one billion one hundred sixteen million five hundred thirty-six thousand sixty-eight |
---|

- 1116536068 has 16 divisors, whose sum is
**2536597440** - The reverse of 1116536068 is
**8606356111** - Previous prime number is
**103**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 37
- Digital Root 1