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Question

The number of solutions of 5r=1cos r x=5 in the interval [0,2π] is


A

0

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B

1

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C

5

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D

10

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Solution

The correct option is B

1


5r=1cos r x=5

cos x+cos 2x+cos 3x+cos 4x+cos 5x=5 which is possible only, when cos x=cos 2x=cos 3x=cos 4x=cos 5x

= 1 and is satisfied by x = 0 only. Hence number of solution = 1.


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