Prove that - sin 7 x - sin 5 x - sin 9x - sin 3x cos 7 x - cos 5 x - cos 9x - cos 3x - tan 6 x

LHS=(sin 7x+sin 5x)+(sin 9x+sin 3x)(cos 7x+cos 5x)+(cos 9x+cos 3x) #160; =2sin 6xcos x+2sin 6xcos 3x2cos 6xcos x+2cos 6xcos 3x #160; =2sin 6x ...

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Prove that : ...

Question

Prove that :
$\frac{(sin 7 x + sin 5 x) + (sin 9 x + sin 3 x)}{(cos 7 x + cos 5 x) + (cos 9 x + cos 3 x)} = tan 6 x$

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\frac{(s i n 7 x + s i n 5 x) + (s i n 9 x + s i n 3 x)}{(c o s 7 x + c o s 5 x) + (c o s 9 x + c o s 3 x)} = t a n 6 x

\frac{sin x - sin 3 x + sin 5 x - sin 7 x}{cos x - cos 3 x - cos 5 x + cos 7 x} = cot 2 x

\frac{sin 5 x + sin 3 x}{cos 5 x + cos 3 x} =

\frac{sin x}{cos 3 x} + \frac{sin 3 x}{cos 9 x} + \frac{sin 9 x}{cos 27 x} = \frac{1}{2} [tan 27 x - tan x]

y = \frac{cos x + cos 2 x + cos 3 x + cos 4 x + cos 5 x + cos 6 x + cos 7 x}{sin x + sin 2 x + sin 3 x + sin 4 x + sin 5 x + sin 6 x + sin 7 x},

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