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

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)`
...
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