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Deepak Bora
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Prove that= √ [ (1 + sin A) / (1 – sin A) ] = sec A + tan A

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CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number  – 30/5/1
Question Number –  30
trigonometric problem
use trigonometric relation

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1 Answer

  1. LHS:
    = √( [1 + sin A] / [1 – sin A])

    = √ { ( [1 + sin A] / [1 – sin A] ) × ( [1 + sin A] / [1 + sin A] ) }

    = √( [1 + sin A]² / [1 – sin² A])

    = √( [1 + sin A]² / cos² A

    = [1 + sin A] / cos A

    = [1 / cos A] + [ sin A / cos A ]

    = sec A +  tan A = RHS
    Hence proved

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