[tex]\bf csc(\theta)=\cfrac{1}{sin(\theta)}
\qquad
% secant
sec(\theta)=\cfrac{1}{cos(\theta)}
\\\\\\
and\qquad sin^2(\theta)+cos^2(\theta)=1
\\\\
-------------------------------\\\\
csc^2(x)sec^2(x)=sec^2(x)+csc^2(x)\\\\
-------------------------------\\\\
sec^2(x)+csc^2(x)\implies \cfrac{1}{cos^2(x)}+\cfrac{1}{sin^2(x)}\implies \cfrac{sin^2(x)+cos^2(x)}{cos^2(x)sin^2(x)}
\\\\\\
\cfrac{1}{cos^2(x)sin^2(x)}\implies \cfrac{1}{cos^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies sec^2(x)csc^2(x)[/tex]
