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Doubt

Ques13. Prove that -
 (sec A - tan A)/(sec A + tan A) = 1 - 2sec A tan A + 2tan2A

Answer Explanation

 (sec2A - tan2A) = 1
 (secA-tanA)(secA+tanA) = 1
 (secA-tanA) = 1/(secA+tanA)
(secA-tanA)2 = 1/(secA+tanA)2  
RHS = 1 -2secAtanA + 2tan2A
       = 1+ tan2A + tan2A - 2secAtanA
       = sec2A + tan2A - 2secAtanA
       = (secA- tanA)2
 LHS = (secA-tanA)/(secA+tanA)  = (secA-tanA)2  { AS 1/(secA+tanA) = (secA-tanA) }

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