C3 Trig questions!!!

Could somebody please help me with this:

7) The angles x and y are acute angles such that sinx= 2 / √5 and cosy= 3 / √10.
a) Show that cos2x=-3/5. (I got -4?!)
b) Find the value of cos2y (Again, i got the wrong answer...).
c) Show without using your calculator, that:
i) tan (x+y) = 7
ii) x-y = π/4.

8) Given that sinxcosy=1/2 and cosxsiny=1/3,
a) show that sin(x+y)=5sin(x-y)
given also that tany=k, express in terms of k,
b) tan x
c) tan 2x

Ohh i see. Thanks!

Could somebody also pls help me with these:
9b)sin3θcos2θ=sin2θcos3θ 0«θ«π
c)sin(θ+40)+sin(θ+50)=0 0«θ«360
e)2sinθ=1+3cosθ 0«θ«360
f)cos5θ=cos3θ 0«θ«π
g)cos2θ=5sinθ -π«θ«π (these last ones are quite similar...i think i need to use Rcos/sin(θ+a), but im not sure...and how do i know which one? What do I do?!?!)

Please help!