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Step-by-step explanation:
LHS
1 + (tan²A / 1 + secA)
tan²A + 1 = sec²A
=> tan²A = sec²A - 1 => (secA - 1)(secA + 1)
Therefore,
1 + (tan²A / 1 + secA)
= 1 + [ (secA - 1)(secA + 1) / ( 1 + secA) ]
(secA + 1) & (1 + secA) will cancel out.
=> 1 + secA - 1
= secA
LHS = RHS
Hence proved
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