# Simplify tan(arcsin(( square root of 2)/2))

Simplify tan(arcsin(( square root of 2)/2))
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Multiply the numerator by the reciprocal of the denominator.
Simplify the denominator.
One to any power is one.
Apply the product rule to .
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Raise to the power of .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Rewrite as .
Any root of is .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
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### Name

Name one billion seven hundred forty-five million seven hundred forty-three thousand three hundred ninety

### Interesting facts

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

### Basic properties

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

### Name

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

### Interesting facts

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

### Basic properties

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

### Name

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

### Interesting facts

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

### Basic properties

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