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 .

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

Simplify.

Subtract from .

Add and .

Apply the distributive property.

Multiply by .

Add and .

Multiply by .

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.

Factor out of .

Rewrite as .

Factor out of .

Rewrite as .

Move the negative in front of the fraction.

Simplify sec(arcsin(x-1))