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06-08-2014
Mathematics

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cos^2 2x−cos^2 6x=sin4x sin8x
please help me prove it

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Everest2017 Everest2017

06-08-2014

Cos² 2x = (1+cos 4x )/2
cos² 6x = (1+cos 12x)/2
subtract to get 1/2 (cos 4x - cos 12x )
= 1/2 (2 sin 4x sin 8x ) as cos A - cos B = 2 [ sin (A+B)/2 sin (A-B)/2 ]
so the answer

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