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\frac{\cos 4 x+\cos 3 x+\cos 2 x}{\sin 4 x+\sin 3 x+\sin 2 x}=\cot 3 x |
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Answer» L.H.S. = (cos4x + cos2x) +cos3x / (sin4x + sin2x) + sin3x = 2cos[(4x+2x)/2].cos[(4x-2x)/2] + cos3x / 2sin[(4x+2x)/2].cos[(4x-2x)/2] + sin3x = 2cos3x.cosx + cos3x / 2sin3x.cosx + sin3x = cos3x(2cosx + 1) / sin3x(2cosx + 1) // Taking common =cos3x(2cosx + 1) / sin3x(2cosx + 1) = cos3x / sin3x = cot3x Hence,L.H.S = R.H.S. |
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