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The number of roots of the equation 3sin...

The number of roots of the equation `3sin^(2)x=8cosx " in" (-(pi)/(2),(pi)/(2))` is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `3(1-cos^(2)x)=8cosx`
`because3cos^(2)x+8cosx-3=0`
`rArr(3cosx-1)(cosx+3)=0`
`therefore"cos"x=(1)/(3)`
`[becausecosxne-3` as cosx cannot be less than -1]
Hence , two solutions exist in a given interval.
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