What is the value of $$[\frac{1}{(1-tan\theta)}]-[\frac{1}{(1+tan\theta)}]$$ ?

Expression : $$[\frac{1}{(1-tan\theta)}]-[\frac{1}{(1+tan\theta)}]$$

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

= $$\frac{2tan\theta}{1-tan^2\theta}$$

= $$(\frac{2sin\theta}{cos\theta})\div(1-\frac{sin^2\theta}{cos^2\theta})$$

= $$(\frac{2sin\theta}{cos\theta})\div(\frac{cos^2\theta-sin^2\theta}{cos^2\theta})$$

= $$(\frac{2sin\theta}{cos\theta})\times(\frac{cos2\theta}{cos^2\theta})$$

= $$\frac{2sin\theta cos\theta}{cos2\theta}$$

= $$\frac{sin2\theta}{cos2\theta}=tan2\theta$$

=> Ans - (C)