Question

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

Answer 1

Answer:

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Answer 2

To prove:

(1 + tan A - sec A) × (1 + tan A + sec A) = 2 tan A

Proof:

LHS

(1 + tan A - sec A) × (1 + tan A + sec A)

...... Using (a+b) (a+b) = (a+b) ²

......... Multiply sec A × sec A

(1 + tan A) ² - sec ²A

....... Using (a+b) ² = a² + b² + 2ab

1 + tan² A + 2 tan A - sec² A

........ Using trigonometry identity 1 + tan² A = sec² A

sec² A + 2 tan A - sec² A

....... + sec² A and - sec² A gets cancelled because of + and - sign

2 tan A

Therefore LHS = RHS

Hence proved that (1 + tan A - sec A) × (1 + tan A + sec A) = 2 tan A

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