Prove the following trigonometrical identities: \[ \frac{\tan ^{2} x}{\tan ^{2} x-1}+\frac{\oper...

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Prove the following trigonometrical identities:
\[
\frac{\tan ^{2} x}{\tan ^{2} x-1}+\frac{\operatorname{cosec}^{2} x}{\sec ^{2} x-\operatorname{cosec}^{2} x}=\frac{1}{\sin ^{2} x-\cos ^{2} x} .
\]
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