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Question
Prove the following identities:
sin4A – cos4A = 2sin2A – 1
Solution
L.H.S. = sin4A – cos4A
= (sin2A)2 – (cos2A)2
= (sin2A + cos2A)(sin2A – cos2A)
= sin2A – cos2A
= sin2A – (1 – sin2A)
= 2sin2A – 1
= R.H.S.
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