Q6 of 46 Page 291

Simplify secA(1 – sinA)(secA + tanA)

By trigonometric identities, sec A = 1/cos A & tan A = sin A/cos A

Using these identities, we have


sec A (1 – sin A)(sec A + tan A) =


⇒ sec A (1 – sin A)(sec A + tan A) =


⇒ sec A (1 – sin A)(sec A + tan A) =


⇒ sec A (1 – sin A)(sec A + tan A) =


⇒ sec A (1 – sin A)(sec A + tan A) = [∵, sin2 A + cos2 A = 1 ⇒ cos2 A = 1 – sin2 A]


⇒ sec A (1 – sin A)(sec A + tan A) = 1


Thus, sec A (1 – sin A)(sec A + tan A) = 1.


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