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

Problem

sin(2*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

4. Substitute the value back into the original expression to get sin(2⋅π/4)

5. Simplify the argument of the sine function.

2⋅π/4=π/2

6. Calculate the final value of sin(π/2)

sin(π/2)=1

Final Answer

sin(2*arccos(√(,2)/2))=1

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