Use the double–angle identity to transform to .

Simplify each term.

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 .

One to any power is one.

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.

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 .

Simplify.

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 .

Simplify.

Cancel the common factor of and .

Multiply by .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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 .

One to any power is one.

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.

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 .

Simplify.

Use the power rule to distribute the exponent.

Apply the product rule to .

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 .

Simplify.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine the numerators over the common denominator.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Expand cos(2arctan(x))