Question

1. (1 - sin A)/(1 + sin A) = (sec A - tan A)2​

Answer 1

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Solution:

L.H.S = (1 - sin A)/(1 + sin A)

= (1 - sin A)2/(1 - sin A) (1 + sin A)

[ Multiply both numerator and denominator by (1 - sin A) ]

= (1 - sin A)2/(1 - sin2 A)

= (1 - sin A)2/(cos2 A)

[Since sin2 θ + cos2 θ = 1 ⇒ cos2 θ = 1 - sin2 θ]

= {(1 - sin A)/cos A}2

= (1/cos A - sin A/cos A)2

= (sec A – tan A)2 = R.H.S

♡ HOPE IT HELPS ♡