Simplify cos(arccos(( square root of 2)/2))

Problem

cos(arccos(√(,2)/2))

Solution

1. Identify the composition of functions. The expression is of the form cos(arccos(x)) where x=√(,2)/2

2. Apply the property of inverse trigonometric functions. For any value x in the domain of arccos(x) which is [−1,1] the identity cos(arccos(x))=x holds true.

3. Verify the domain. Since √(,2)/2≈0.707 it falls within the interval [−1,1]

4. Evaluate the expression by applying the identity directly.

Final Answer

cos(arccos(√(,2)/2))=√(,2)/2

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