Question

cos x+cos 3x+cos 5x/sin x+sin 3x+sin 5x

Answer 1

see solve like this:
cos x+cos 5x=2cos3xcos2x
and
sin x +sin5x=2sin3xcos2x


Now,
2cos3xcos2x + cos3x/2sin3xcos2x +sin3x
take , cos3x common from numerator and sin3x from denominator
(2cos2x + 1)cos3x/(2cos2x + 1)sin3x

See my friend 2cos2x +1 is common both in numerator and denominator, cancel it.
We get cos3x/sin3x=cot3x

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