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If the function f(x)=(Ksinx+2cosx)/(sinx...

If the function `f(x)=(Ksinx+2cosx)/(sinx+cosx)` is strictly increasing for all values of `x ,` then `K<1` (b) `K >1` `K<2` (d) `K >2`

A

`klt1`

B

`kle2`

C

`kge3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
4
Since `f(x) = (K sin x+ 2 cosx)/(sin x+ cos x)` is strictly increasing
`f(x) gt 0 for all x`
or `(k-2)/(sinx _++ cosx)^(2)gt 0 for all x`
or `k-2gt 0 or kgt2`
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