Trig Q 3

the basic process of finding the answer to the question
Q what is the max value of

a Sinx + b Cos x is √a²+b² and the min value is -√a²+b²

so by this method we get the maximum value as

=√12 + 16 + 16√3 +16
=√44+16√3
=2√11+4√3 is the maximum value
and the minimum value is -2√11+4√3

i had done the same thing ...but did not match any of the options

is the ans is d