The maximum value of the function f(x)= sin (x+π /6)+ cos (x+π /6) in the interval (0, text π /2) occurs at

Question

The maximum value of the function f(x)= sin (x+π /6)+ cos (x+π /6) in the interval (0, text π /2) occurs at (A)  π /12  (B)  π /6  (C)  π /4  (D)  π /3

Tardigrade Admin · Accepted Answer

Maximum value of f(x)=√2, when x+π /6=π /4 i.e., when x=(π /12)

Q. The maximum value of the function
$f (x) = sin (x + π /6) + cos (x + π /6)$
in the interval $(0, π /2)$ occurs at

$π /12$

$π /6$

$π /4$

$π /3$

Maximum value of $f (x) = 2,$
when $x + π /6 = π /4$ i.e.,
when $x = \frac{π}{12}$

Q. The maximum value of the function f(x)=sin(x+π/6)+cos(x+π/6) in the interval (0,π/2) occurs at

π/12

π/6

π/4

π/3