What is [(1 + sin A)/ (1- sin A )] – [(1 – sin A)/(1 +sin A)] equal to ?

What is  [(1 + sin A)/ (1- sin A )] – [(1 – sin A)/(1 +sin A)]   equal to ?

  1. Sec A – tan A
  2.  2 sec A . tan A
  3.  4 sec A. tan A
  4.  4 cosec A . cot A
jagadeesh Default Asked on 24th July 2015 in Maths.
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  • 1 Answer(s)

    Answer: (3) 4 sec A. tan A
    Explanation:-
    [(1 + sin A)/ (1- sin A )] – [(1 – sin A)/(1 +sin A)]
    = [(1 + sin A) (1 + sin A)/(1 –  sin A) (1 +  sin A)] – [(1 – sin A) (1 –  sin A)/(1 +  sin A) (1 –  sin A)]
    =[1 + sin2 A + 2  sin A)/(1 –  sin2 A) – (1 + sin2 A – 2  sin A)/(1 –  sin2 A)
    =(1 + sin2 A + 2  sin A – 1 – sin2A + 2 sin A)/ (1 – sin2A)
    = (2 sin A + 2sinA )/cos2A
    = 4sin A/cos2A
    = 4 sin A/cos A x cos A
    = 4 sec A tan A.
    Hence, the answer is (3) 4 sec A. tan A.

    Anurag Mishra Professor Answered on 24th July 2015.
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