If $$\frac{Sin\theta + Cos\theta}{Sin\theta - Cos\theta}= 3$$ then the value of $$Sin^4\theta$$ is:

Expression : $$\frac{Sin\theta + Cos\theta}{Sin\theta - Cos\theta}= 3$$

=> $$sin\theta+cos\theta=3sin\theta-3cos\theta$$

=> $$3sin\theta-sin\theta=cos\theta+3cos\theta$$

=> $$2sin\theta=4cos\theta$$

=> $$sin\theta=2\sqrt{1-sin^2\theta}$$

Squaring both sides, we get :

=> $$sin^2\theta=4(1-sin^2\theta)$$

=> $$sin^2\theta=4-4sin^2\theta$$

=> $$sin^2\theta+4sin^2\theta=4$$

=> $$5sin^2\theta=4$$

=> $$sin^2\theta=\frac{4}{5}$$

=> Ans - (A)