(cos x + cos y)² + (sin x – sin y)² = 4 cos² (x + y)/2

Question

TextSum to Product Transformation Formulae

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Prove that (cos 7x + cos 5x) / (sin 7x – sin 5x) = cot x

Prove that (sin 5x – 2sin 3x + sin x) / (cos 5x – cos x) = tan x

sin2 x + 2 sin 4x + sin 6x = 4 cos² x sin 4x

TextSum to Product Transformation Formulae

cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)

(cos 9x – cos 5x) / (sin 17x – sin 3x) = – sin 2x / cos 10x

(sin 5x + sin 3x) / (cos 5x + cos 3x) = tan 4x