Find the Exact Value cos(arctan(1))

Problem

cos(arctan(1))

Solution

1. Identify the inner value by letting θ=arctan(1)

2. Determine the angle θ in the interval (−π/2,π/2) such that tan(θ)=1

3. Evaluate the angle to find θ=π/4

4. Substitute the angle back into the original expression to get cos(π/4)

5. Calculate the exact value of the cosine function for the given angle.

Final Answer

cos(arctan(1))=√(,2)/2

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