Question: Find the Wronskian of the given pair of functions.
$$cos^2(x), 1+cos(2x)$$
$$W = \det
\begin{vmatrix}
cos^2(x) & 1+cos2x \\
-2sin(x)cos(x) & -2sin(2x)
\end{vmatrix}
= \det
\begin{vmatrix}
cos^2(x) & 2cos^2(x) \\
-sin(2x) & -2sin(2x)
\end{vmatrix}
$$
\begin{align}
\implies W &= -2cos^2(x)sin2(x)-(-sin(2x))(2cos^2(x))\notag\\
&= 2sin(2x)(-cos^2(x)+cos^2(x))\notag\\
&= 2sin(2x)\cdot0\notag\\
&= 0\notag
\end{align}
