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

Problem

sec(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 (or 45.

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

5. Apply the reciprocal identity sec(θ)=1/cos(θ)

6. Calculate the final value using cos(π/4)=√(,2)/2

sec(π/4)=1/cos(π/4)

1/√(,2)/2=2/√(,2)

2/√(,2)=√(,2)

Final Answer

sec(arccos(√(,2)/2))=√(,2)

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