How do I convert cosx+(sqrt3)sinx to 2sin(x+30)?

If you use the trig identity:  sin(A + B) = sin(A)cos(B) + cos(A)sin(B):

Substituting  A with x  and  B with 30:

--->   2[ sin(x + 30) ]  =  2[ sin(x)cos(30) + cos(x)sin(30) ]

Since    sin(30) = 1/2   and   cos(30) = √(3)/2

--->   2[ sin(x)·√(3)/2 + cos(x)·(1/2) ]

Using the distributive property with 2:

--->   √(3)sin(x) + cos(x)