A wave represented by the given equation y=acos(kx−ω t) is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is

Since the point x = 0 is a node and reflection is taking place from point x = 0.  This means that reflection must be taking place from the fixed end and hence the reflected ray must suffer an additional phase change of π or a path change of λ2. So, if yincident=acos(kx−ω t)⇒yreflected=acos(−kx−ω t+π)=−acos(ω t+kx)