Answer
$cot^{2}\theta+sec^{2}\theta=tan^{2}\theta+csc^{2}\theta$
Work Step by Step
Need to prove the identity $cot^{2}\theta+sec^{2}\theta=tan^{2}\theta+csc^{2}\theta$
In order to prove this, take left side isolate.
$cot^{2}\theta+sec^{2}\theta=(csc^{2}\theta-1)+(tan^{2}\theta-1)$
$cot^{2}\theta+sec^{2}\theta=csc^{2}\theta+tan^{2}\theta$
Hence, $cot^{2}\theta+sec^{2}\theta=tan^{2}\theta+csc^{2}\theta$