Simplify csc(arccos(( square root of 3)/2))

Problem

csc(arccos(√(,3)/2))

Solution

1. Evaluate the inner inverse trigonometric function arccos(√(,3)/2)

2. Identify the angle θ in the interval [0,π] such that cos(θ)=√(,3)/2

3. Determine that θ=π/6 (or 30 because cos(π/6)=√(,3)/2

4. Substitute this value back into the original expression to get csc(π/6)

5. Apply the reciprocal identity csc(θ)=1/sin(θ)

6. Calculate the final value using sin(π/6)=1/2 which means csc(π/6)=1/(1/2)=2

Final Answer

csc(arccos(√(,3)/2))=2

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