If A+B=225°, then find the value of #(cot A/(1+cot A))(cot B/(1+cot B))#?

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Answer 1 · 2018-06-03T14:54:11

#ans=1/2#

#rarrA+B=225°#

#rarrcot(A+B)=cot225°=cot(180°+45°)=cot45°=1#

#rarr(cotA*cotB-1)/(cotA+cotB)=1#

#rarrcotA*cotB-1=cotA+cotB#

#rarrcotA+cotB+1=cotA*cotB....(1)#

Now,

#rarr(cotA*cotB)/((1+cotA)*(1+cotB))#

#=(cotA*cotB)/(1+cotB+cotA+cotA*cotB)#

#=(cotA*cotB)/(cotA*cotB+cotA*cotB)....#using #(1)#

#=(cancel(cotAcotB))/(2cancel(cotAcotB))=1/2#