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If the function f(x) = 2cotx+(2a+1) ln|c...

If the function `f(x) = 2cotx+(2a+1) ln|cosec x| + (2-a)x` is strictly decreasing in `(0, pi/2)` then range of a is

A

`[0,oo)`

B

`(-oo,0]`

C

`(-oo,oo)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)=2 cit x+(2a+1)log_(e)|"cosec x"|+(2-a)x`
`rArr" "f'(x)=-"2 cosec"^(2)x-(a+1)cosx+(2-a)`
`=-2cot^(2)x-(2a+1)cotx-a`
`=(cot x +a)(-2cot x-1)le 0 " in "(0,(pi)/(2))`
`therefore" "cotx+a ge 0" in "(0,(pi)/(2))`
Hence, age0`
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