Answer :

Take L.H.S.


cos A + cos 3A + cos 5A + cos 7A


= (cos 3A + cos A) + (cos 7A + cos 5A)






= 2 cos 2A cos A + 2 cos 6A cos A


= 2 cos A (cos 6A + cos 2A)






= 4 cos A cos 2A cos 4A


= R.H.S.


Hence Proved


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