Prove -

1) $\displaystyle sec (u) + tan (u) = \frac {1} {sec(u) - tan(u)} $

2) $\displaystyle sec (u) + cosec (u)cot(u) = sec(u)cosec^2(u) $

3) $\displaystyle sin^2 (u)(1+sec^2 (u) ) = sec^2 (u) - cos^2 (u) $

4) $\displaystyle \frac {1-cos (u)} { sin(u)} = \frac {1} {cosec(u) + cot(u)} $

Any help appreciated