Finding Wronskian of [cos(theta)]^2 and 1+cos(2theta)

[physstudent1]

Homework Statement

take the wronskian of [cos(theta)]^2 and 1+cos(2theta)

Homework Equations

The Attempt at a Solution

so I set up the determinant

[cos(theta)]^2 1+cos(2theta) as my y1 and y2 respectively and
-2cos(theta)sin(theta) and -sin(2theta) as my y1 and y2 prime respectively

i get my determinant to be -2cos(theta)sin(theta)*[cos(theta)]^2 +2cos(theta)sin(theta)*(1+cos(2theta)) the answer in the back says it should be 0. So I'm assuming I have to do something with basic trig identities to get it to 0? I can't seem to get it to go to 0 though I've been trying for 30 minutes :(. Can anyone offer some insight?

 

[AEM]

Homework Statement

take the wronskian of [cos(theta)]^2 and 1+cos(2theta)

Homework Equations

The Attempt at a Solution

so I set up the determinant

[cos(theta)]^2 1+cos(2theta) as my y1 and y2 respectively and
-2cos(theta)sin(theta) and -sin(2theta) as my y1 and y2 prime respectively

i get my determinant to be -2cos(theta)sin(theta)*[cos(theta)]^2 +2cos(theta)sin(theta)*(1+cos(2theta)) the answer in the back says it should be 0. So I'm assuming I have to do something with basic trig identities to get it to 0? I can't seem to get it to go to 0 though I've been trying for 30 minutes :(. Can anyone offer some insight?

For one thing, I think your y2 prime should be -2sin(2 theta). (You briefly forgot the chain rule).

 

[physstudent1]

...wow I am an idiot! thanks I got it to simplify to 0 now haha sigh.