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prove that sinx - siny/cosx+ cosy=tan(x-y/2)

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prove that following question

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express the following product of sines or cosines or sine and cosine functions sin 5x - sin 3x

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express the following product of sines or cosines or sine and cosine functions sin 7x + sin 3x

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express the following product of sines or cosines or sine and cosine functions cos 5x- cos 7x

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express the following product of sines or cosines or sine and cosine functions cos 5x + cos 3x

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