Question 916899
ow do I verify this identity?
(tan of theta + cotangent of theta) ^2 = sec ^2 of theta + csc ^ 2 of theta 
***
use x for theta
{{{(tanx+cotx)^2=sec^2(x)+csc^2(x)}}}
start with left side:
{{{(tanx+cotx)^2=tan^2(x)+2tanxcotx+cot^2(x)}}}
tanx*cot=1
using pythagorean identities:
tan^2(x)=sec^2(x)-1
cot^2(x)=csc^2(x)-1
{{{(tanx+cotx)^2=sec^2(x)-1+2+csc^2(x)-1=sec^2(x)+csc^2(x)}}}
verified: left side = right side