If w is complex cube root of 1, then cos⁡(1−w)1−w2+(2−w)2−w2+….+(10−w)10−w2π900=

∑r=110 (r−w)r−w2=∑r=110r2+∑r=110r+∑1r=110=450 since w+w2=−1,w3=1 now given question=cosπ2=0

If w is complex cube root of 1, then cos⁡(1−w)1−w2+(2−w)2−w2+….+(10−w)10−w2π900=

∑r=110 (r−w)r−w2=∑r=110r2+∑r=110r+∑1r=110=450 since w+w2=−1,w3=1 now given question=cosπ2=0

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If w is complex cube root of 1, then $\cos (((1 - w) (1 - w^{2}) + (2 - w) (2 - w^{2}) + \dots . + (10 - w) (10 - w^{2})) \frac{π}{900}) =$

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$\frac{\sqrt{3}}{2}$

answer is B.

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$\sum_{r = 1}^{10} (r - w) (r - w^{2}) = \sum_{r = 1}^{10} r^{2} + \sum_{r = 1}^{10} r + {\sum 1}_{r = 1}^{10} = 450 since w + w^{2} = - 1, w^{3} = 1 n o w g i v e n q u e s t i o n = \cos (\frac{π}{2}) = 0$

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If w is complex cube root of 1, then cos⁡(1−w)1−w2+(2−w)2−w2+….+(10−w)10−w2π900=

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If w is complex cube root of 1, then $\cos (((1 - w) (1 - w^{2}) + (2 - w) (2 - w^{2}) + \dots . + (10 - w) (10 - w^{2})) \frac{π}{900}) =$