If √5 tan θ = 5 sin θ, then what is the value of (sin$$^{2}$$ θ - cos$$^{2}$$θ)?

Given : $$\sqrt5tan\ \theta=5sin\ \theta$$

=> $$\frac{sin\ \theta}{cos\ \theta}=\sqrt5sin\ \theta$$

=> $$cos\ \theta=\frac{1}{\sqrt5}$$

=> $$cos^2\ \theta=\frac{1}{5}$$ ---------------(i)

Now, $$sin^2\ \theta=1-cos^2\ \theta$$

=> $$sin^2\ \theta=1-\frac{1}{5}=\frac{4}{5}$$ --------------(ii)

Subtracting equation (i) from (ii), we get :

$$\therefore$$ $$(sin^2\ \theta-cos^2\ \theta)=\frac{4}{5}-\frac{1}{5}=\frac{3}{5}$$

=> Ans - (A)