Hard Math Problem

Question

Each of the following expressions can be written in the form a sin 2x + b cos 2 x + c

a) 2 cos² x + 4sin x cos x

b) -2sin x cos x -4sin²x

Answer 1

2cos²x = 1+cos 2x (start with cos²x - sin²x = cos 2x

sin 2x = 2sin x cos x

Hence the first expression can be written 1+cos 2x + 2 sin 2x = 2 sin 2x + cos 2x + 1

You now have enough information to do the 2nd one by yourself!