# Toronto Math Forum

## MAT244--2019F => MAT244--Test & Quizzes => Quiz-3 => Topic started by: baixiaox on October 11, 2019, 01:59:16 PM

Title: tut0401 Quiz3
Post by: baixiaox on October 11, 2019, 01:59:16 PM
Find the Wronskian of the given pair of functions:
$$cos^2(x),\,1+cos(2x)$$
$$W= \begin{vmatrix} cos^2(x)&1+cos(2x)\\ -2cos(x)sin(x)&-2sin(2x)\\ \end{vmatrix}\\ = \begin{vmatrix} cos^2(x)&1+cos(2x)\\ -sin(2x)&-2sin(2x)\\ \end{vmatrix}\\ cos(2x)=2cos^2(x)-1\\ sin(2x)=2sin(x)cos(x)\\ =-2cos^2(x)sin(2x)+sin(2x)+sin(2x)cos(2x)\\ =-sin(2x)[2cos^2(x)-1-cos(2x)]\\ =-sin(2x)[cos(2x)-cos(2x)]\\ =-sin(2x)\times0\\ =0\\ \$$
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