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( cos 4x + cos 3x + cos 2x )/( sin 4x + ...

`( cos 4x + cos 3x + cos 2x )/( sin 4x + sin 3x + sin 2x) = cot3x`

Text Solution

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LHS `=(cos4x+cos3x+cos2x)/(sin4x+sin3x+sin2x)`
`=(cos3x+(cos4x+cos2x))/(sin3x+(sin4x+sin2x))`
`=(cos3x+2cos(4x+2x)/(2)cos(4x-2x)/(2))/(sin3x+2sin(4x+2x)/(2)cos(4x-2x)/(2))`
`(cos3x+2cos3xcosx)/(sin3x+2sin3xcosx) = (cos3x(1+2cosx))/(sin3x(1+2cosx))`
`(cos3x)/(sin3x) = cot3x` = RHS. Hence Proved.
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