1. Prove

Question

sin - cos +1/ sin + cos - 1 = sin +1/cos

2. 1+ sin/ 1- sin = (sec + tan)^2

Thanks!!

Answer 1

Your lack of brackets make your equations totally ambiguous.
Secondly your trig ratios have no argument, sin and cos by themselves are meaningless
that's like saying

5 + √

I happen to know the second one , so
(1+ sinØ)/(1 - sinØ) = (secØ + tanØ)^2

LS = (1+ sinØ)/(1 - sinØ) * (1+sinØ)/(1+sinØ)
= (1 + sinØ)^2 /(1 - sin^2Ø)
= (1 + 2sinØ + sin^2 Ø)/ cos^2 Ø
= 1/cos^2 Ø + 2sinØ/cos^2 Ø + sin^2 Ø/cos^2 Ø
= sec^2 Ø + 2tanØsecØ + tan^2 Ø
= (secØ + tanØ)^2
= RS