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Question
Prove the following:
sin2A cos2B + cos2A sin2B + cos2A cos2B + sin2A sin2B = 1
Solution
L.H.S. = sin2A cos2B + cos2A sin2B + cos2A cos2B + sin2A sin2B
= (sin2A cos2B + sin2A sin2B) + (cos2A sin2B + cos2A cos2B)
= sin2A (cos2B + sin2B) + cos2A (sin2B + cos2B)
= sin2A + cos2A ...[∵ sin2A + cos2A = 1]
=1
=R.H.S.
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