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

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.

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, .

Add and .

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.

Add and .

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.

Rewrite the expression.

Cancel the common factor.

Rewrite the expression.

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