tanx = -5/12; x in quad IV

so I got tan 2x = -120/119 but I don't understand how to get sin2x and cos2x.

cosx = 5/9; x in quad I

Like the previous problem, I am able to get cos2x, which is -31/81, but I don;t know how to get the other 2 functions.

Lastly,

sinx = 2sin x/2 cos x/2

I'm not really sure hot to prove this. It looks like a double angle sin identity.