What about questions like these?

1-2sinx - cosx (where x = theta)

It can either be 2sinx + cosx = 1 or cosx + 2sinx = 1

For this question i rearranged it into 2sinx + cosx = 1 and used Rsin(x+a).

2 = Rcosa , 1 = Rsina

a = 26.6

How do i continue when a number is present on the RHS even before I equated it to 1 or -1 to find the max and min. points?

Edit:

I read somewhere before that we ignore the number for these type of questions. In that case I tried,

Stuck here.

will give 90-26.6 = 63.4 which is not the maximum point(243.4)