Question

if Sin[2x]=2Sin[x]Cox[x]

then if

10*Cos[Sqrt[5]x] + [20/Sqrt[5]]*Sin[Sqrt[5]x]

Subbing 10=K*Sin[Z] && [20/Sqrt[5]]=K*Cos[Z]

What will it be in the simplest form?

I have worked this out BUT I would like to confirm my results please!!