Prove the following trigonometrical identities: \[ \sin ^{2} x \cos ^{2} y-\cos ^{2} x \sin ^{2}...

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Prove the following trigonometrical identities:
\[
\sin ^{2} x \cos ^{2} y-\cos ^{2} x \sin ^{2} y=\sin ^{2} x-\sin ^{2} y
\]
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