The general solution of the equation `8 cos x cos 2x cos 4x = sin 6x//sin x` is

Options

A. `x=(n pi//7)+(pi//21), AA n in Z`
B. `x=(2pi//7)+(pi//14), AA n in Z`
C. `x=(n pi//7)+(pi//14), AA n in Z`
D. `x=(n pi)+(pi//14), AA n in Z`

Answer

C

Explanation

The given equation is
`8 sin x cos x cos 2x cos 4 x= sin 6x (sin x ne 0)`
`rArr sin 8x= sin 6x`
`rArr 2 cos 7x sin x =0`
As `sin x ne 0, cos 7x=0`
or `7x=n pi +pi//2, n in Z`
i.e. `x= n pi//7+pi//14, n in Z`