Answer
$\dfrac{1}{1-\sin^{2}x}=1+\tan^{2}x$
Work Step by Step
$\dfrac{1}{1-\sin^{2}x}=1+\tan^{2}x$
Substitute $1-\sin^{2}x$ by $\cos^{2}x$:
$\dfrac{1}{\cos^{2}x}=1+\tan^{2}x$
Substitute $\dfrac{1}{\cos^{2}x}$ by $\sec^{2}x$:
$\sec^{2}x=1+\tan^{2}x$
Since $\sec^{2}x=1+\tan^{2}x$, the identity is proved.
$1+\tan^{2}x=1+\tan^{2}x$
