If (sin θ+ cos θ)/(sinθ- cosθ) =3 :

If (sin θ+ cos θ)/(sinθ- cosθ) =3 then the value of sin4 θ is:

  1. 3/5
  2. 1/5
  3. 2/5
  4. 4/5
Anurag Mishra Professor Asked on 11th December 2015 in Maths.
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1 Answer(s)

Answer:  (4) 4/5

Explanation:-
(sinθ + cosθ)/(sinθ – cosθ) = 3
(sinθ + cosθ) (sinθ + cosθ)/(sinθ – cosθ)(sinθ + cosθ) = 3
(sin²θ + cos²θ + 2 sinθ cosθ)/ sin²θ – cos²θ = 3
As we know that sin²θ + cos²θ = 1

Then, (1 + 2 sinθ cosθ)/(sin²θ – cos²θ) = 3
As we know that sin²θ – cos²θ = cos 2θ & 2 sinθ cosθ = sin 2θ

Then, (1 + sin2θ)/cos2θ = 3

Anurag Mishra Professor Answered on 11th December 2015.
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