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$T h e n u m b e r o f s o l u t i o n s o f \sum_{r = 1}^{5} \cos r x = 5 i n t h e i n t e r v a l [0, 2 π] i s$

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Correct option is D

∑r=15cosrx=5⇒cosx+cos2x+cos3x+cos4x+cos5x=5which is possible only when cosx=cos2x=cos3x=cos4x=cos5x=1 and is satisfied by x=0 and x=2π

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The number of solutions of∑r=15cosrx=5 in the interval 0,2π is

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$T h e n u m b e r o f s o l u t i o n s o f \sum_{r = 1}^{5} \cos r x = 5 i n t h e i n t e r v a l [0, 2 π] i s$