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cos(x)cos(2x)cos(3x)=1/4. Find the gener...

`cos(x)cos(2x)cos(3x)=1/4`. Find the general solution.

Text Solution

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`cos x cos 2x cos 3x = 1/4`
or `2(2 cos x cos 3x) cos 2x=1`
or `2(cos 4x+cos 2 x) cos 2x=1`
or `2(2 cos^(2) 2x-1+cos 2x) cos 2x=1`
or `4 cos^(3) 2x+2 cos^(2) 2x-2 cos 2x-1=0`
or `(2cos^(2)2x-1)(2 cos 2x+1)=0`
or `cos 4x(2 cos 2x+1)=0`
`:. cos 4x=0 or cos 2x=-1//2`
`:. 4x=(2n+1) pi/2, 2x=2mpi pm (2pi)/3, m , n in Z`
or `x=(2n+1) pi/8, x= mpi pm pi/3`
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