- #1

- 29

- 2

## Homework Statement

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, sin

^{2}x and cos

^{2}x.

## Homework Equations

s

_{1}sin2xcos2x+s

_{2}sin2x+s

_{3}cos2x+s

_{4}sin

^{2}x+s

_{5}cos

^{2}x=0

I need to prove that all s

_{1},s

_{2},s

_{3},s

_{4}and s

_{5}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:

(s

_{1}/2 + s

_{2})sin2x + (s

_{3}-s

_{4}/2 + s

_{5}/2)cos2x + [(s

_{4}+s

_{5})/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.

Last edited: