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