Question

Which expression is equivalent to cos(1.4x) – cos(0.6x)?

Answer 1

\[-2\sin (x) \sin (0.8x)\]

Answer 2

Use the (Simpson) formula for the difference of two cosines:

\(\cos a-\cos b=-2\sin\frac{a+b}{2}\sin\frac{a-b}{2}\)

Just put in a=1.4x and b=0.6x!

Answer 3

BTW it is a good idea to learn all the trig identities by heart.
Then, when confronted with a problem, you will get ideas to solve them.
If you have to look up these formulas every time, you will always have trouble solving trig problems.