Verified answer

cos3x+cos5x+cos7x=(cos 3x +cos 7x)+cos 5x=2cos 5x cos 2x+cos 5x=cos 5x(2cos 2x+1)

sin3x+sin5x+sin7x=(sin 3x+sin 7x)+sin 5x=2sin 5xcos2x+sin 5x=sin 5x (2cos x+1)

(cos3x+cos5x+cos7x)/(sin3x+sin5x+sin7x)=(cos 5x(2cos 2x+1))/(sin 5x (2cos x+1))=

cos (5x) / sin (5x) =ctg (5x)

(cos3x+cos5x+cos7x)/(sin3x+sin5x+sin7x)=(2cos4xcosx+cos7x)/(2sin4xcosx+sin7x)=(cos4x+cos7x)/(sin4x+sin7x)=(2cos5.5xcos1.5x)/(2sin5.5xcos1.5x)=cos5.5x/sin5.5x=ctg5.5x