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सिद्ध कीजिए:`tan^(2)theta+cot^(2)theta=sec^(2)thetacosec^(2)theta-2.`

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`tan^(2)theta+cot^(2)theta=sec^(2)thetacosec^(2)theta-2`
बायाँ पक्ष `=tan^(2)theta+cot^(2)theta`
`=sec^(2)theta-1+cosec^(2)theta-1`
`=sec^(2)theta+cosec^(2)theta-2`
`=(1)/(cos^(2)theta)+(1)/(sin^(2)theta)-2=(sin^(2)theta+cos^(2)theta)/(costhetasin^(2)theta)-2`
`=(1)/(cos^(2)thetasin^(2)theta)-2=(sin^(2)theta+cos^(2)theta)/(cos^(2)thetasin^(2)theta)-2sec^(2)thetacosec^(2)theta-2`दायाँ पक्ष।

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