Q

# Find the general solution for each of the following equation cos 4x = cos 2x

Find the general solution for each of the following equation

Q (5)  $\small \cos 4x = \cos 2x$

Views

cos4x = cos2x
cos4x - cos2x = 0
We know that
$\cos A - \cos B = -2\sin\frac{A+B}{2}\sin\frac{A-B}{2}$
We use this identity
$\therefore$  cos 4x - cos 2x  = -2sin3xsinx
$\Rightarrow$ -2sin3xsinx = 0    $\Rightarrow$   sin3xsinx=0
So, by this we can that either
sin3x = 0     or    sinx = 0
3x = $n\pi$                 x = $n\pi$
x = $\frac{n\pi}{3}$                x = $n\pi$

Therefore, the general solution is

$x=\frac{n\pi}{3}\ or\ n\pi \ where \ n\in Z$

Exams
Articles
Questions