In order to prove that sin(t), cos(t) and cos(2*t) are independent, you have to show that if
f(t) = a*sin(t) + b*cos(t) + c*cos(2*t)
for scalars a, b, c in IR is the identical null function (i.e. f(t) = 0 for all t), then a,b and c must all be zero.
So assume f is the null function.
Then the expression a*sin(t) + b*cos(t) + c*cos(2*t) will give zero especially when you insert t=0, t=pi/2 and t=pi.
See what follows for a,b and c by setting up the corresponding (3x3) linear system of equations for a, b and c and solving it - maybe by determining the rank of the coefficient matrix, if your assignment says you should do so.
