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Question
Prove the following:
cos 4x = 1 – 8sin2 x cos2 x
Solution
L.H.S. = cos 4x
= cos 2(2x)
= 1 – 2 sin2 2x [∵ cos 2A = 1 – 2 sin2 A]
= 1 – 2(2 sin x cos x)2 [∵ sin2A = 2sin A cosA]
= 1 - 2 [4 sin2 x cos2 x] = 1 – 8 sin2 x cos2 x
= R.H.S.
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