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Prove (tanA+cosec B)^2-(cot B-secA)^2= 2...

Prove `(tanA+cosec B)^2-(cot B-secA)^2= 2 tan A cotB(cosec A+secB)`

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LHS
`=(tanA+cosecB)^2-(cotB-secA)^2`
`=tan^2A-sec^2A+cosec^2B-cot^2B+2tanAcosecB-2cotBsecA` `=-1+1+2tanAcosecB-2cotBsecA`
`=2tanAcoseccB*cotB/cotB+2cotBsecAtanA/tanA`
`=2tanAcotB((cosecB)/cotB+secA/tanA)`
`=2tanAcotB(secB+cosecA)`.
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