If Cosθ +Sin θ= m and Sec θ+ Cosec θ=n then the value of n(m²-1) is equal to:

  1. 2n
  2. 4mn
  3. mn
  4. 2m
Anurag Mishra Professor Asked on 10th December 2015 in Maths.
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  • 1 Answer(s)

    Answer:  (4) 2 m 

    Explanation:-
    Cosθ +Sin θ= m ………………………… (1)
    and Sec θ+ Cosec θ=n
    Sec θ+ Cosec θ=n
    1/Cosθ + 1/Sinθ = n
    (Sinθ + Cosθ)/Cosθ Sinθ = n

    n(m² – 1)
    Put the value of m = Cosθ +Sin θ & n = (Sinθ + Cosθ)/Cosθ Sinθ
    Then, (Sinθ + Cosθ)/Cosθ Sinθ {(Cosθ +Sin θ)² – 1}
    = (Sinθ + Cosθ)/Cosθ Sinθ x {Cos²θ + Sin²θ + 2 Cosθ Sinθ – 1}
    = (Sinθ + Cosθ)/Cosθ Sinθ x (1 + 2 Cosθ Sinθ – 1}
    = (Sinθ + Cosθ)/Cosθ Sinθ x (2 Cosθ Sinθ)
    = 2 (Sinθ + Cosθ)
    From equation (1),
    = 2 m

    Hence, the correct answer is option (4) 2 m.

    Anurag Mishra Professor Answered on 10th December 2015.
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