Given that $\sin\theta = 4\sin(\theta – 60°)$, show that $2\sqrt{3}\cos(\theta) = \sin(\theta) $

Question

The answer I get when I try to simplify the first equation gives me $2\sin\theta – 2\sqrt{3}\cos\theta,$ which clearly is not the same as $2\sqrt{3}\cos\theta$.

Or am I missing something obvious?

I've attached a screenshot of the question directly from the book.

Thanks in advance.

Answer 1

You have $\sin\theta=4\sin(\theta-60^o)=2\sin\theta-2\sqrt3\cos\theta$.

Now subtract $\sin\theta$ from both sides:

$0=\sin\theta-2\sqrt3\cos\theta,$

or $2\sqrt3\cos\theta=\sin\theta$.