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The number of solutions of sum(r=1)^5cos...

The number of solutions of `sum_(r=1)^5cosrx=5` in the interval `[0,2pi]` is 0 (b) 2 (c) 5 (d) 10

A

0

B

2

C

5

D

10

Text Solution

Verified by Experts

The correct Answer is:
B
`sum_(r=1)^(5) cos r x=5`
`rArr 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` and `x=2pi`.
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