1. The problem statement, all variables and given/known data 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. 2. Relevant equations s1sin2xcos2x+s2sin2x+s3cos2x+s4sin2x+s5cos2x=0 I need to prove that all s1,s2,s3,s4 and s5 must be equal to zero for the above equation to be true. 3. 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.