Draw a triangle in the plane with vertices <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> , <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and the origin. Then <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is the angle between the positive x-axis and the ray beginning at the origin and passing through <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> . Therefore, <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>arcsin</mi><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mrow></mfrac></mstyle></math> .

Multiply the numerator by the reciprocal of the denominator.

One to any power is one.

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

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

Rewrite <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Cancel the common factor.

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

Evaluate the exponent.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Cancel the common factors.

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

Cancel the common factor.

Rewrite the expression.

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.

Simplify the numerator.

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

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Any root of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Combine and simplify the denominator.

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

Raise <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>2</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><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Cancel the common factor.

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

Evaluate the exponent.

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor.

Rewrite the expression.

Cancel the common factor.

Rewrite the expression.

Do you know how to Simplify tan(arcsin(( square root of 2)/2))? 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 seven hundred forty-five million seven hundred forty-three thousand three hundred ninety |
---|

- 1745743390 has 16 divisors, whose sum is
**3149439408** - The reverse of 1745743390 is
**0933475471** - Previous prime number is
**443**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | one billion nine hundred thirty-four million four hundred five thousand nine hundred forty-nine |
---|

- 1934405949 has 32 divisors, whose sum is
**2976952576** - The reverse of 1934405949 is
**9495044391** - Previous prime number is
**337**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 48
- Digital Root 3

Name | one billion four hundred ten million two hundred twenty-six thousand four hundred ninety-one |
---|

- 1410226491 has 8 divisors, whose sum is
**1915779600** - The reverse of 1410226491 is
**1946220141** - Previous prime number is
**53**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 30
- Digital Root 3