sec^2 x + csc ^2 x =
1 / cos^2 x + 1/sin^2x =
[sin^2 x + cos^2 x ] / [ sin^2x * cos^2x] =
1 / [sin^2x * cos^2x] =
1/sin^2x * 1/cos^2x =
csc^2 x * sec^2 x [other answers are possible ]
\(\color{aqua}sec^2\theta + csc^2\theta=\color{aqua}\frac{1}{cos^2\theta}+\frac{1}{sin^2\theta}=\frac{sin^2\theta+cos^2\theta}{sin^2\theta cos^2\theta}= \frac{1}{sin^2\theta cos^2\theta}\space OR\space sec^2\theta csc^2\theta\)
(Same as CPhill's answer, just using LaTeX to make it clearer.)
:D
.