Which of the following identities, wherever defined, hold(s) good?

1   cos2⁡α−sin2⁡αsin⁡αcos⁡α=2cot⁡2α2   1+t1−t−1−t1+t,  where        t=tan⁡α=(1+t)2−(1−t)21−t2=4t1−t2=2×2tan⁡α1−tan2⁡α=2tan⁡2α         Hence, (2) is incorrect. 3    1+t1−t+1−t1+t=(1+t)2+(1−t)21−t2=21+t21−t2=2cos⁡2α=2sec⁡2α           Hence, (3) is correct. 4   tan⁡α+cot⁡α=1cos⁡αsin⁡α=2sin⁡2α=2cosec⁡2α         Hence, (4) is incorrect.