Prove the following trigonometrical identities: \[ \sec ^{2} x+\operatorname{cosec}^{2} x=\sec ^...

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Prove the following trigonometrical identities:
\[
\sec ^{2} x+\operatorname{cosec}^{2} x=\sec ^{2} x \operatorname{cosec}^{2} x
\]
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