The expression √(1+sinθ/ 1- sinθ) + √(1-sinθ/ 1+ sinθ) is equal to :

  1. 2 sec θ
  2. 2 tan θ
  3. 2 (1-sin θ)/cos θ
  4. 2 sin θ
Anurag Mishra Professor Asked on 27th December 2015 in Maths.
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1 Answer(s)

Answer: (1) 2 secθ

Explanation:-
√(1+sinθ/ 1- sinθ) + √(1-sinθ/ 1+ sinθ)
= √(1 + sinθ) (1 + sinθ)/(1 – sinθ)(1 + sinθ) + √(1-sinθ) (1- sinθ)/(1+ sinθ)(1-sinθ)
= √[(1 + sinθ)²/1 – sin²θ] + √[(1- sinθ)²/1 – sin²θ]
= √[(1 + sinθ)²/cos²θ] + [(1- sinθ)²/cos²θ]
= (1 + sinθ)/cosθ  + (1- sinθ)/cosθ
= (1 + sinθ + 1- sinθ)/cosθ
= 2/cosθ
= 2 secθ

Then, the value of √(1+sinθ/ 1- sinθ) + √(1-sinθ/ 1+ sinθ) is equal to 2 secθ.

Hence, the correct answer is option (1) 2 secθ.

Anurag Mishra Professor Answered on 27th December 2015.
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