1.

If `A+B=90` then prove that `sqrt((tanAtanB+tanAcotB)/(sinAsecB))=secA`

Answer» `tan(90-A)=cotA`
`tan B= cotA`
`sinB=cosA`
`cosecB=secA`
`tanA=cotB`
`sinA=cosB`
`coseccA=secB`
LHS
`=sqrt((tanAcotA+tanAtanA)/(sinAcosecA))`
`=sqrt(1+tan^2A)`
`=sqrt(sec^2A)`
`=secA`


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