I just found a generalised formula to find the range of the functions of the form:
\[f(x)=a\cos x + b\sin x + c\]
The range of the above function would be: .
Here's what I did;
1. Multiply and divide the function by ;
2. Now, say that there exists a right triangle whose sides are , such that;
3. Substitute the above values in the function to get:
4. Now let us say that the angle , thus the maximum value of and the minimum value of , hence;