If `a <= 3cosx+5sin(x-pi/6) <= b` for all `x,` then `(a,b)` is

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)`