# Simplify tan(arcsin(( square root of two) divide two))

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 .
First, multiply the numerator by the denominator's reciprocal.
Clarify the denominator.
One raised to any power equals one.
Apply the product rule to .
Should be rewritten as .
Rewrite as .
Apply the power rule when multiplying the exponents, .
The common factor should be canceled of .
Cancel the common factor.
First, divide by .
Solve the exponent.
Raise to the power of .
The common factor should be canceled and .
Factor out of .
The common factors should be canceled.
Factor out of .
Cancel the common factor.
Reformulate 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.
First, multiply by .
Add numerators over the common denominator.
Clarify the numerator.
First, multiply by .
Subtract from .
Rewrite as .
Any root of is .
Multiply by .
Add and then simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to Add 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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