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If the sum of all the solutions of the equation `8 cosx.(cos(pi/6+x)cos(pi/6-x)-1/2)=1` in `[0,pi]` is `k pi` then k is equal to

A

`(8)/(9)`

B

`(20)/(9)`

C

`(2)/(3)`

D

`(13)/(9)`

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The correct Answer is:
D
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