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## Homework Statement

If 1/2<=x<=1

, then cos

^{-1}[ x/2 + (√(3-3x

^{2}))/2] + cos

^{-1}x is equal to?

## Homework Equations

## The Attempt at a Solution

Substituting x=cosθ

= cos

^{-1}(cosθ) + cos

^{-1}[ cos(θ)/2 + (√(3(1-cos

^{2}(θ)))/2]

= θ + cos

^{-1}[cos (π/3) cos θ + sin (π/3) sinθ]

= θ + cos

^{-1}[cos (θ -(π/3)]

= 2θ -(π/3)

= 2 cos

^{-1}x -(π/3)

But the correct answer according to the book is π/3. Please help me understand what I've done wrong.

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