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Prove `: cot^(2) theta-tan^(2)theta=cosec^(2)theta-sec^(2)theta`

Answer» Proof: `LHS =cot^(2) theta-tan^(2)theta`
`=(cosec^(2)theta-1)-(sec^(2)theta-1)…{:[(cosec^(2)theta=1+cot^(2)theta),(sec^(2)theta=1+tan^(2)theta)]:}`
`=cosec^(2) theta-1-sec^(2)theta+1`
`=cosec^(2) theta-sec^(2) theta`
`=RHS`
`:.cot^(2) theta-tan^(2)theta=cosec^(2)theta-sec^(2)theta`.


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