Simplify cos(arctan( square root of 3))

Problem

cos(arctan(√(,3)))

Solution

1. Evaluate the inner expression arctan(√(,3)) by identifying the angle θ in the interval (−π/2,π/2) such that tan(θ)=√(,3)

2. Identify the angle as θ=π/3 (or 60 because tan(π/3)=√(,3)

3. Substitute the angle back into the outer trigonometric function to get cos(π/3)

4. Calculate the value of cos(π/3) using the unit circle or special right triangles.

5. Determine that cos(π/3)=1/2

Final Answer

cos(arctan(√(,3)))=1/2

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