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Question
Prove the following:
cos22x − cos26x = sin4x sin8x
Solution
L.H.S. = cos22x − cos26x
= (cos 2x)2 − (cos 6x)2
= (cos 2x + cos 6x) (cos 2x − cos 6x)
= `[2cos((2x + 6x)/2) cos((2x - 6x)/2)]*[2sin((2x + 6x)/2)sin((6x - 2x)/2)]`
= [2 cos 4x cos (− 2x)] [2 sin 4x sin 2x]
= (2 cos 4x cos 2x) (2 sin 4x sin 2x)
= (2 sin 2x cos 2x) (2 sin 4x cos 4x)
= sin 4x sin 8x
= R.H.S.
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