The difference between the greatest and least value of function `f(x)=cosx+1/2cos2x-1/3cos3x` is

Explanation

function is `f(x) = cosx + 1/2cos2x - 1/3 cosx`

`f'(x)= -sinx -2/2sin2x + 3/2sin3x`

`= -sinx -sin2x +sin3x`

`= -(sinx + sin2x) + sin3x`

`=-(2sin((3x)/2)cos((x)/2)) + 2sin((3x)/2)cos((3x)/2)`

`= 2sin((3x)/2)[cos((3x)/2)- cos(x/2)]`

`= 2sin((3x)/2)*2sin(2x)*sin(x)`

`= 4sinxsin2xsin((3x)/2)`

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