If `alt=3cosx+5sin(x-pi/6)lt=b` for all `x` then `(a , b)` is `(-sqrt(19),sqrt(19))` (b) `(-17 ,17)` `(-sqrt(21),sqrt(21))` (b) `non eoft h e s e`

Options

A. `(-sqrt(19)sqrt(19))`
B. `(-17,17)`
C. `(-sqrt(21),sqrt(21))`
D. none of these.

Answer

A

Explanation

`f(x)=3cos x+5sin(x-pi//6)`
`=(1)/(2)cosx+5xx(sqrt(3))/(2)sinx`
Then, `-sqrt(((1)/(2))^(2)+((5sqrt(3))/(2))^(2))lef(x)lesqrt(((1)/(2))^(2)+((3sqrt(3))/(2))^(2))`
or `-sqrt(19)lef(x)lesqrt(19)`