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The sum of the absolute maximum and absolute minimum values of the function f(x) = tan –1 (sin x – cos x) in the interval [0, π ] is

1. 0
2. tan –1 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 1 – 4 π
3. cos –1 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 3 1 – 4 π
4. 12 π −

Correct answer: cos –1 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 3 1 – 4 π

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