Prove that (1 + tan A – sec A) × (1 + tan A + sec A) = 2 tan A

1.	Prove that (1 + tan A – sec A) × (1 + tan A + sec A) = 2 tan A
Answer» LHS = (1 + tan A – sec A) × (1 + tan A + sec A) (x – y) (x + y) = x² – y² here x = 1 + tan A y = sec A LHS = (1 + tan A)² – (sec A)² = 1 + tan² A + 2 tan A – sec² A = sec² A + 2 tan A – sec² A (1 + tan² A = sec² A) = 2 tan A = RHS Hence, proved.

Answer»

LHS = (1 + tan A – sec A) × (1 + tan A + sec A)

(x – y) (x + y) = x² – y²

here x = 1 + tan A

y = sec A

LHS = (1 + tan A)² – (sec A)²

= 1 + tan² A + 2 tan A – sec² A

= sec² A + 2 tan A – sec² A (1 + tan² A = sec² A)

= 2 tan A = RHS

Hence, proved.

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Prove that (1 + tan A – sec A) × (1 + tan A + sec A) = 2 tan A

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