Question 172756
I'm going to use {{{alpha}}} instead of theta, because this system won't render theta for some reason.


{{{(sec(alpha)/sin(alpha))(cot(alpha)/csc(alpha))=csc(alpha)}}}


{{{sec(alpha)=1/cos(alpha)}}}, {{{cot(alpha)=cos(alpha)/sin(alpha)}}}, and {{{csc(alpha)=1/sin(alpha)}}}


So:

{{{((1/cos(alpha))/sin(alpha))((cos(alpha)/sin(alpha))/(1/sin(alpha)))=(1/sin(alpha))/(sin(alpha)/sin(alpha))=1/sin(alpha)=csc(alpha)}}}


QED