# Expand sin(arcsin(x)-arccos(x)) Apply the difference of angles identity.
Simplify terms.
Simplify each term.
The functions sine and arcsine are inverses.
The functions cosine and arccosine are inverses.
Multiply by .
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 .
Divide by .
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 .
Divide by .
Multiply .
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 .
Simplify.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Multiply by .
Multiply by .
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply .
Multiply by .
Multiply by .
Expand sin(arcsin(x)-arccos(x))

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