a. Express 1.5 sin 2x + 2 cos 2x in the form R sin (2x + α), where R > 0 and 0 < α < π/2 , giving your values of R and α to 3 decimal places where appropriate.

b. Express 3 sin x cos x + 4 cos² x in the form a sin 2x + b cos 2x + c, where a, b and c are constants to be found.

c. Hence, using your answer to part a, deduce the maximum value of 3 sin x cos x + 4 cos² x.