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

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