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The value of x which satisfies 8^(1+cos...

The value of x which satisfies `8^(1+cos xcos^(2)x +….)` = 64 in `[-pi,pi]` is

A

`+-(pi)/2,+-(pi)/3`

B

`+-(pi)/3`

C

`+-(pi)/2,+-(pi)/6`

D

`+-(pi)/6,+-(pi)/3`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `8^(1+cos x + cos^(2)x+…..)=8^(2)`
`implies1/(8^(1-cosx))=8^(2)`
`[ :' cos x !=1,` as for `cos x=1+1+1+……!=2,` nad `|cosx|lt1]`
`implies1/(1-cosx)=2`
`implies2cos x=1`
`impliescosx=1/2`
`impliesx=+-(pi)/3`
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