prove (csc theta+1)/(csc theta-1) = (sec theta+tan theta)^2

As usual for this type of problem start by replacing the tan, sec, and csc functions with their sine and cosine equivalents. Then simplify. For example, the left hand side can be manipulated like this:


\frac {\csc \theta+1}{\csc \theta -1} = \frac {\frac 1 {\sin \theta} +1}{\frac 1 {\sin \theta} -1} = \frac {1 + \sin \theta} {1 - \sin \theta}


Do the same thing to the right hand side, and you should get an expression whose numerator and denominator can be factored and simplified. Post back with what you get.