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Show that (i) cos x+cos y=2 cos (x+y)/(...

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)`

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