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Let \(f\) be the function defined on \([0, \pi]\) by:$$ f(x) = (1 - \sin(x)) \cos(x) $$
    1. Calculate the derivative \(f'(x)\).
    2. Show that \(f'(x) = (2\sin(x) + 1)(\sin(x) - 1)\).
    1. Determine the sign of \(2\sin(x) + 1\), then the sign of \(\sin(x) - 1\) on the interval \([0, \pi]\).
    2. Deduce the variations of \(f\) on \([0, \pi]\).

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