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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    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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