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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