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Question
Prove the following:
`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`
Solution
L H.S. = `(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x)`
= `((cos4 x + cos2x)+cos 3x)/((sin4x + sin 2x) + sin 3x)`
= `(2cos ((4x + 2x)/2) cos ((4x - 2x)/2) + cos 3x)/(2sin ((4x + 2x)/2) cos ((4x - 2x)/2) + sin 3x)`
= `(2cos 3x cosx+cos3x)/(2sin 3x cosx + sin3x)`
= `(cos3x (2cosx+ 1))/(sin3x(2cosx +1))`
= `(cos3x)/(sin3x)`
= cot 3x = R.H.S.
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