Let F= {f|f: R→ R} denote the vector space of real-valued functions. Which of the following are linearly independent subsets in

Question

Let F= {f|f: R→ R} denote the vector space of real-valued functions.
Which of the following are linearly independent subsets in F?
S = {sin x, cos x}
T = {1, sin x, cos x}
U = {1, sin² x, cos²x}
V = {1,2 sin² x, 3 cos² x}
mark (X) the correct answer:
A S and T
BS and U
CS and V
DT and U
ET and V
FU and V

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