Answer
$\sec^2 B=\frac{1}{1-\sin^2 B}$
Work Step by Step
Start with the right side:
$\frac{1}{1-\sin^2 B}$
$=\frac{1}{\cos^2 B}$
$=(\frac{1}{\cos B})^2$
$=\sec^2 B$
Since this equals the left side, the identity has been proven.
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