The equation for a light wave of amplitude a propagating in the x-direction is (x,t)=A sin(t-kx), (1) where k=2/ is the wave number, =2f is the angular frequency, and t is the time. If we choose x=0 as the location of the observer then (x=0,t)=A sint. In the case of the precision interferometer, the wave of amplitude A from mirror M_1 arrives at the observer with phase _1, and the wave with the same amplitude A from M_2 arrives with phase _2. Show that the resulting disturbance can be expressed as (x=0,t)=2A sin(t+(_1+_2)/2) cos((_1-_2)/2). (2)