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

Problem

tan(arccos(√(,2)/2))

Solution

1. Evaluate the inner inverse trigonometric function arccos(√(,2)/2)

2. Identify the angle θ in the interval [0,π] such that cos(θ)=√(,2)/2

3. Determine that θ=π/4 because cos(π/4)=√(,2)/2

4. Substitute the angle back into the outer function to get tan(π/4)

5. Calculate the value of tan(π/4) which is 1

Final Answer

tan(arccos(√(,2)/2))=1

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