Question

Find the general solution of $\cos 3x=\cos 2x$. Then solution is$\frac{\alpha n\pi }{5}$ then $\alpha$ =

Answer 1

$cos3x-cos2x=0-2sin\left(\frac{3x+2x}{2}\right)sin\left(\frac{3x-2x}{2}\right)=0sin\left(\frac{5x}{2}\right)sin\left(\frac{x}{2}\right)=0\therefore sin\left(\frac{5x}{2}\right)=0\left(\frac{5x}{2}\right)=n\pi \therefore x=\left(\frac{2n\pi }{5}\right)\therefore sin\left(\frac{x}{2}\right)=0\left(\frac{x}{2}\right)=n\pi \therefore x=2n\pi combiningbothresultx=\left(\frac{2n\pi }{5}\right)$