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

1  tan⁡θ=1−cos⁡2θsin⁡2θ.   Hence, option (1) is correct.2    sin⁡2θ=2tan⁡θ1+tan2⁡θcos⁡2θ=1−tan2⁡θ1+tan2⁡θtan⁡2θ=2tan⁡θ1−tan2⁡θ        Hence, option (2) is correct.3   tan⁡3θ=sin⁡3θcos⁡3θHence, option (3) is correct.4   sin⁡θ=1/3  which is rational but cos⁡3θ=cos⁡θ4cos2⁡θ−3 which is irrational.       Hence, option (4) is incorrect.