Prove that the followint is an identity (A is a positive constant).
A*sin(x)*sin(wt)+A*cos(x*)cos(wt)=A*cos(wt-x)
+128656 From a trig identity,
cos(Θ) = cos (-Θ) therefore
cos (wt-x) = cos(-(wt-x)) = cos(x-wt) so we have .. (using the angle difference indentity for the cosine)
Acos(x-wt) = A[cos(x)cos(wt) + sin(x)sin(wt)] = Asin(x)sin(wt) + Acos(x)cos(wt) ....and that = the left hand side
+128656 From a trig identity,
cos(Θ) = cos (-Θ) therefore
cos (wt-x) = cos(-(wt-x)) = cos(x-wt) so we have .. (using the angle difference indentity for the cosine)
Acos(x-wt) = A[cos(x)cos(wt) + sin(x)sin(wt)] = Asin(x)sin(wt) + Acos(x)cos(wt) ....and that = the left hand side
