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

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

A

` pm pi/2 , pm pi/3`

B

` pm pi/3 `

C

` pm pi/2 , pi/6`

D

` pm pi/6 , pm pi/3 `

Text Solution

Verified by Experts

The correct Answer is:
b
Given , `8^(1+cosx+cos^(2)x_...)= 8^(2) rArr 8^(1/(1-cosx))=8^(2)`
`[ :' cos != 1, "as for" cos x = 1+1+1+... != 2, and |cos x| lt 1]`
` rArr 1/(1-cos x)=2`
` rArr 2 cos x =1`
` rArr cos x =1/2 rArr x = pm pi/3`
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