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

Problem

cos(arcsin(√(,2)/2))

Solution

1. Identify the inner value √(,2)/2 and determine the angle θ=arcsin(√(,2)/2)

2. Recall the unit circle values for the inverse sine function, where the range is restricted to [−π/2,π/2]

3. Determine that sin(θ)=√(,2)/2 corresponds to the angle θ=π/4 (or 45.

4. Substitute the angle back into the outer function to evaluate cos(π/4)

5. Evaluate the cosine of π/4 which is √(,2)/2

Final Answer

cos(arcsin(√(,2)/2))=√(,2)/2

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