Question

prove that 4 cos12 degrees × cos 48 degrees × cos72 degrees = cos36 degrees

Answer 1

You might have heard of the identity
$\cos( \alpha ) \times \cos(60 - \alpha ) \times \cos(60 + \alpha ) \\ = \frac{ \cos( 3\alpha ) }{4}$
If not, don't worry, it's very easy to prove.
You may try it yourself. With that being said, the question is
$4 \cos(12) \times \cos(48) \times \cos(72) \\ = 4( \cos(12) \times \cos(60 - 12) \times \cos(60 + 12) \\ = 4 \times \frac{ \cos(3 \times 12) }{4} \\ = \cos(36)$