it can be easily solved by finding maxima and minima
the given expression translates to 3-cos x – cos2x
Differentiating and euating to 0.
sinx + 2cos x sin x = 0
sinx (1+ 2 Cos x)= 0
sinx = 0 or cosx = -1/2
cos x =1 or cos x = -1/2
Cos x = 1 will give minimum value and cos x =-1/2 will give max.
Substituting this in expresstion 3-cos x – cos2x
Max Value = 3 + ½ -1/4 = 13/4
and Min value = 3 – 1 – 1 = 1
Hence ratio of max and min = 13/4.
I have confirmed thing by plotting the graph of entire function.
