Prove that in the set of real-valued functions {sin t, sin 2t , sin t cos t} is not a basis for the space spanned by the set. Then find the basis for that space. [Hint: can one of the functions in the...

Please include properties and rules for each step.

I need explains for each step

Extracted text: Prove that in the set of real-valued functions {sin t, sin 2t , sin t cos t} is not a basis for the space spanned by the set. Then find the basis for that space. [Hint: can one of the functions in the set be written as a linear combination of the others?]