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For which of the following values of x i...

For which of the following values of `x` is `(0^(@) lt x lt 90^(@)) 16^(1+cos x + cos^(2)x + cos^(3) x + … oo)` = 256 ?

A

`30^(@)`

B

`45^(@)`

C

`60^(@)`

D

`15^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
`16^(1+cosx + cos^(2) x+ cos^(3)x + ...oo)` = 256
`16^((1)/(1-cosx)) = 256 rArr 16^((1)/(1-cosx)) = 16^(2)`
`rArr (1)/(1-cosx) =2 rArr 1-cosx = (1)/(2)`
`1-(1)/(2) = cos x`
`(1)/(2) = cosx rArr x = 60^(@)`.
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