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18.(sin x-sin y)/(cos x+cos y)=tan(x-y)/...

18.(sin x-sin y)/(cos x+cos y)=tan(x-y)/(2)

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Show that (i) cos x+cos y=2 cos (x+y)/(2) cos (x-y)/(2) (ii) cos x-cos y=-2 sin (x+y)/(2) sin (x-y)/(2) (iii) sin x+sin y=2 sin (dot(x)+y)/(2) cos (x-y)/(2) (iv) sin x-sin y=2 cos (x+y)/(2) sin (x-y)/(2)