How do double angle identities work? (Trigonometry)

Question

I don't understand how to do maths mostly because I don't understand why formulae works they way they do or the reasoning behind equations and etc.

I tried explain the (sin 2 theta) double-side identity but failed:

Hypothetically if:

opp = 1
adj = 2
hyp = 3

(sin 2 theta) = (2 sin theta)(cos theta)

(opp/hyp)*2 = 2(opp/hyp)*(adj/hyp)
(1/3)*2 = 2(1/3)*(2/3)
2/3 =/= 4/9

How do the double-angle identities work?

Answer 1

What the sin 2θ = 2sinθ * cosθ formulas is saying is.....for example

sin 40 = 2sin 20 * cos 20    or

sin 170 = sin (2*85) = 2*sin 85 * cos 85

 

In your example, you doubled the sin....not the angle.

 

Hope this helps.