# Ask Uncle Colin: Can you prove $\sin(2x) \equiv 2\sin(x)\cos(x)$? | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

Dear Uncle Colin,

I find it easier to remember trigonometric identities if I can ‘see’ how they fit together. I’m expected to know that $\sin(2x) \equiv 2\sin(x)\cos(x)$, but haven’t been able to prove it. Any ideas?

— Geometry? Right Angles? How About Medians?

Hi, GRAHAM!

My favourite proof jumps out from a picture like this one: