In the vector space of all real-valued functions, find a

basis for the subspace spanned by {sin(t); sin(2t); sin(t)cos(t)}

I can clearly see that sin(2t) can be written as 2*sin(t)cos(t), so that means that 2*sin(t)cos(t) and sin(t)cos(t) are linearly dependent sets.

Am I right so far?

So where do I go from here?