Question 1088220
If all we are looking for is the maximum value, then a shift in x of pi/6 will not change the amplitude, only the phase.
Therefore, we only need to find the maximum value of the function sin(x) + cos(x)
The max. value is obtained where df/dx = 0 = cos(x) - sin(x)
Thus tan(x) = 1 -> x = pi/4
f(pi/4) = 1/sqrt(2) + 1/sqrt(2) = 2/sqrt(2) = sqrt(2)
Ans: sqrt(2)