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Question
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
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Solution
LHS = ( 1 + tan A)2 + (1 - tan A)2
= 1 + 2 tan A + tan2A + 1 - 2 tan A + tan2A
= 2( 1 + tan2A)
= 2 sec2A
= RHS
Hence proved.
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