MAT244--2019F > Quiz-3

TUT0402 question

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shangluy:
Find the Wronskian of $cos^2\theta$ and $1 + cos2\theta$

Let $f = cos^2\theta$ and $g = 1 + cos2\theta$, then

since $W = fg' - f'g$, we get
\begin{align*}
W &= cos^2\theta(-2sin2\theta) - (-sin2\theta)(1 + cos2\theta)\\
&= -2cos^2\theta sin2\theta + sin2\theta(1 + cos2\theta)\\
Therefore the Wronskian of $cos^2\theta$ and $1 + cos2\theta$ is $0$