Which of the following statements are always correct (where Q denotes the set of rationals)? 

a. $\tan \mathrm{\theta }=\frac{1-\cos 2\mathrm{\theta }}{\sin 2\mathrm{\theta }}$ Hence, option (a) is correct.

b.

     $\begin{array}{r}\sin 2\mathrm{\theta }=\frac{2\tan \mathrm{\theta }}{1+{\tan }^2\mathrm{\theta }}\\ \cos 2\mathrm{\theta }=\frac{1-{\tan }^2\mathrm{\theta }}{1+{\tan }^2\mathrm{\theta }}\\ \tan 2\mathrm{\theta }=\frac{2\tan \mathrm{\theta }}{1-{\tan }^2\mathrm{\theta }}\end{array}$

      Hence, option (b) is correct.

c. $\tan 3\mathrm{\theta }=\frac{\sin 3\mathrm{\theta }}{\cos 3\mathrm{\theta }}$ Hence, option (c) is correct.

d. $\sin \mathrm{\theta }=1/3$ which is rational but $\cos 3\mathrm{\theta }=\cos \mathrm{\theta }\left(4{\cos }^2\mathrm{\theta }-3\right)$ which is irrational.

     Hence, option (d) is incorrect.