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The number of solutions of the equation ...

The number of solutions of the equation `cos^(2)((pi)/(3)cos x - (8pi)/(3))=1` in the interval `[0,10pi]` is

A

1

B

3

C

5

D

7

Text Solution

Verified by Experts

The correct Answer is:
C
`cos^(2)((pi)/(3)cos. X-(8pi)/(3))=1`
`rArr (pi)/(3)cos. X-(8pi)/(3)=k pi, (k in Z)`
`rArr cos x = 3k + 8, k in Z`
`rArr cos x = -1`, when `k = -3`
`rArr` there are 5 solutions for `x in [0, 10pi]`
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