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Simplify sec A (1 – sin A) (sec A + tan A)

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Simplify sec A (1 – sin A) (sec A + tan A)

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L.H.S. = sec A (1 – sin A) (sec A + tan A)

= (sec A – sec A . sin A) (sec A + tan A) 

= (sec A – \(\frac{1}{cos\, A}\) . sin A) (sec A + tan A) 

= (sec A – tan A) (sec A + tan A) 

= sec2 A – tan2 A [∵ sec2 A – tan2 A = 1] 

= 1

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