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If f(x) =sin x +log(e)|sec x + tanx|-2x ...

If `f(x) =sin x +log_(e)|sec x + tanx|-2x` for `x in (-(pi)/(2),(pi)/(2))` then check the monotonicity of f(x)

Text Solution

Verified by Experts

The correct Answer is:
Stictly increasing
`f'(x) =cosx + (sec x tanx +sec^(2)x)/(sec x +tan x )-2`
`=cos x+ sec x-2`
`=(cos^(2)x-2 cosx+1)/(cos x)`
`=(cosx-1)^(2)/(cosx)>=0` for all `x in (-(pi)/(2),(pi)/(2))`
`therefore` f(x) is increasing function
Also f'(x) =0 at x=0 only
`therefore` f(x) is strictly increasing function
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