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The greatest possible value of the expre...

The greatest possible value of the expression `tanx+cotx+cosx` on the interval `[pi//6, pi//4]` is

A

`(12)/(5)sqrt2`

B

`(11)/(6)sqrt2`

C

`(12)/(5)sqrt3`

D

`(11)/(6)sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=tanx+cotx+cosx`
`=(2)/(sin2x)+cosx`
Both `(2)/(sin2x) and cos x` decreasing on `[pi//6,pi//4]` and thus the greatest value occurs at `x=pi//6`
i.e. `(2)/(sinpi//3)+cospi//6=(4)/(sqrt3)+(sqrt3)/(2)=(11)/(2sqrt3)=(11sqrt3)/(6)`
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