Let, f(x) = sin(x + π /3) + cos(x + π /3) Here, sin(x + π /3) + cos(x + π /3) ⇒√2[1∕√2(sin(x+π∕3)+1∕√2cos(x+π∕3)] ⇒√2[cos(π∕4)×sin(x+π∕3)+sin(π∕4)×cos(x+π∕3)] ⇒√2[sin(x+π∕3+π∕4)] Now, we know sin x has maximum value at x = π/2 ∴For maximum value of sin(x + π /3) + cos(x + π /3), x + π/3 + π/4 = π/2 ⇒ x = π/2 - 7π/12 ⇒ x = π/12 Hence, option (4) is correct.