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The function f(x)=sqrt(3)sin x-cos x wil...

The function `f(x)=sqrt(3)sin x-cos x` will increase monotically in the interval(s)

A

`0le x le (pi)/(2)`

B

`-(pi)/(3)le x le (2pi)/(3)`

C

`(5pi)/(3)le x le(8pi)/(3)`

D

`0 le x le pi`

Text Solution

Verified by Experts

The correct Answer is:
B, C
`f(x)=2((sqrt(3))/(2)sin x-(1)/(2)cos x)=2 sin (x-(pi)/(6))`
`rArr f(x)` will increase monotically if `-(pi)/(2)le x -(pi)/(6)le(pi)/(2)` and `(3pi)/(2) le x -(pi)/(6)le(5pi)/(2)`
`rArr -(pi)/(3)le x le (2pi)/(3)` nd `(5pi)/(3)le x le (8pi)/(3)`
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