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Prove that (i) 2 cos x cos y=cos (x+y)...

Prove that
`(i) 2 cos x cos y=cos (x+y)+cos (x-y)`
(ii) `-2 . sin x sin y=cos (x+y)-cos (x-y)`
(iii) `2 sin x cos y=sin (x+y)+sin (x-y)`
(iv) `2 cos x sin y=sin (x+y)-sin (x-y)`

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