How do you verify #tanx / (1-cosx) = cscx (1+secx)#?
Use trick algebra while working with the RHS.
There probably is a more efficient method. Nonetheless, here is my work to make the right hand side look like the left:
Multiply both numerator and denominator by (cos x -1)
--also took out a negative to fit with Pythagorean identity #1
Then multiply both the numerator and the denominator by (1/sin x )
Now do same with (1/cos x )
Hope this helps :-)