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Question
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
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Solution
L.H.S. = (sec A − tan A)2 (1 + sin A)
`(1/cos "A" - sin "A"/cos "A")^2 (1 + sin "A")`
= `((1 - sin "A")/cos "A")^2 (1 + sin "A")`
= `((1 - sin "A")(1 - sin "A")(1 + sin "A"))/cos^2"A"`
= `((1 - sin "A")(1 - sin^2 "A"))/cos^2"A"`
= `((1 - sin "A")cos^2"A")/cos^2"A"`
= (1 − sin A) R.H.S.
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