There's no reason to give you the problem from scratch. I just want to show that 5 trigonometric functions are linearly independent to prove what the problem wants. These 5 functions are sin2xcos2x. sin2x, cos2x, sin2x and cos2x.
I need to prove that all s1,s2,s3,s4 and s5 must be equal to zero for the above equation to be true.
The Attempt at a Solution
I used the trigonometric formulas and came to this:
(s1/2 + s2)sin2x + (s3-s4/2 + s5/2)cos2x + [(s4+s5)/2] = 0.
We usually use the derive here but it doesn't seem to help.
Edit: Oh, yeah. We haven't been taught the matrix yet.