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Let f(x) = log (sin x+ cos x), x in x (-...

Let `f(x) = log (sin x+ cos x), x in x (-pi/4,(3pi)/(4))` Then f is stricly increasing in the interval

A

`(-pi/4,pi/4)`

B

`(0,(3pi)/8)`

C

`(pi/2,(3pi)/(4))`

D

`(-pi/8, pi/8)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have` f(x) log (sinx+ cos x ),`
`therefore f'(x)=(cos x-sin x)/(sin x + cos x )=(1 -tanx )/(1+ tan x )=tan (pi/4-x)`
For f(x) to be increasing,we must have
`f(x) gt 0 `
`rArr (pi/4-x)gt 0 `
`rArr 0 lt pi/4 -x lt pi/2 rArr - pi/4 lt -x lt pi/4`
`rArr -pi/4 lt x lt pi/4 rArr x in (-pi/4,pi/4)`
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