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If `A={x:(pi)/(6) lt x lt (pi)/(3)}` and `f(x) =cosx-x(1+x),` then `f(A)` is equal to :

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If `A={x:(pi)/(6) lt x lt (pi)/(3)}` and `f(x) =cosx-x(1+x),` then `f(A)` is equal to :
A. `[(pi),(6),(pi)/(3)]`
B. `[(-pi)/(3),(-pi)/(6)]`
C. `[(1)/(2)-(pi)/(3)(1+(pi)/(3)),(sqrt(3))/(2)-(pi)/(6)(1+(pi)/(6))]`
D. None of these
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Correct Answer - c
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