Find the general solution for each of the following equation 

Q (5)  \small \cos 4x = \cos 2x

Answers (1)

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   

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