sin x + cos x = sqrt(2)* sin(x+45)
Now, let see how to plot the graph of sinx + cosx
Step1: Get the zero points of the curve.
i.e sin x + cos x=0
sinx = -cosx
x = 3pi/4, 7pi/4,....
Step2: Putting zeroes in the function, I will get f(x) = sinx + cos x=1 and putting x = 2pi f(x) =1. Thus those are the end points.
Step 3: Get the points where the curve is either maxima or minima,
Differentiating, we get
thus, x = pi/4, 5pi/4
All the points would be the domian of the function f(x), since it is defined everywhere.