Prove that 1+sinx/1-sinx -1-sinx/1+sinx=4tanxsecx

If interpreted as shown, the order is shown in the lines following
1+sin(x)/1-sin(x)-1-sin(x)/1+sin(x)
=1 + ((sin(x))/1)  - sin(x) -1 - (sin(x)/1)  + sin(x)
which is completely meaningless for the purpose of this question.

The left-hand side is

common denominator is (1-sin(x))(1+sin(x)), so


  using a^2-b^2=(a+b)(a-b)




Therefore