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Solve the equation 2*arctan(2x + 1) = arccos(x).

1. x = 0
2. x = 1
3. x = -1
4. No solution

Correct answer: x = 0

Solution

Apply cos to both sides. The left side becomes (1 - t²)/(1 + t²) with t = 2x+1. Equate to x, solve, then verify the candidate respects the principal-value ranges.

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