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Question
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
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Solution
L.H.S. = (1 – tan A)2 + (1 + tan A)2
= (1 + tan2A – 2 tan A) + (1 + tan2A + 2 tan A)
= 2(1 + tan2A)
= 2 sec2A
= R.H.S.
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