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If `A+B=225` show that `cotA/(1+cotA).cotB/(1+cotB)=1/2`

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If `A+B=225` show that `cotA/(1+cotA).cotB/(1+cotB)=1/2`
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LHS
`cotA/(1+cotA)*cotB/(1+cotB)`
`=(1/tanA)/(1+1/tanA)*(1/tanB)/(1+1/tanB)`
`=1/(1+tanA)*1/(1+tanB)`
`A+B=225^o`
`B=225^o-A`
`tanB=tan(225^o-A)`
`tanb=tan(45^o-A)`
`tanB=tan(225-A)`
`1/(1+tanA+(1+tanA)tanB)=1/(1+1)=1/2`=RHS
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