# If (sin θ+ cos θ)/(sinθ- cosθ) =3 :

If (sin θ+ cos θ)/(sinθ- cosθ) =3 then the value of sin^{4} θ is:

- 3/5
- 1/5
- 2/5
- 4/5

**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