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The number of solutions of 12 cos^(3) x-...

The number of solutions of `12 cos^(3) x-7 cos^(2) x+4 cos x=9` is

A

0

B

2

C

infinite

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The given equation is
`(cos x-1) (12 cos^(2) x+5 cos x+9)=0`
`rArr cos x=1` only as the other factor gives imaginary roots
`rArr x= 2n pi, n in Z`
Hence, it has infinite solutions as `n in Z`.
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