If $$tan(\theta)tan(5\theta)=1$$, then what is the value of $$sin 2\theta$$ ?

Given : $$tan(\theta)tan(5\theta)=1$$

Using, $$tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}$$

$$tan(\theta+5\theta)=\frac{tan(\theta)+tan(5\theta)}{1-tan(\theta)tan(5\theta)}$$

=> $$tan(6\theta)=\frac{tan(\theta)+tan(5\theta)}{1-1}$$

=> $$tan(6\theta)=\infty$$

=> $$tan(6\theta)=tan(90^\circ)$$

=> $$6\theta=90^\circ$$

=> $$\theta=\frac{90^\circ}{6}=15^\circ$$

$$\therefore$$ $$sin(2\theta)=sin(2\times15^\circ)$$

= $$sin(30^\circ)=\frac{1}{2}$$

=> Ans - (B)