Question

√sec+1/sec-1=cot+cosec

Answer 1

first of all you have to rationalize the LHS
after some steps you will get
$\sqrt{(sec + 1) {}^{2} } \div \sqrt{sec {}^{2} - 1 }$
sec2-1 =tan2
then u get
$sec + 1 \div tan$
after removing root
you have to separate it as
$sec \div tan + 1 \div tan$

at last u get
sec/tan=cosec
1/tan = cot