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

Question

15165 views around the world

You can reuse this answer
Creative Commons License

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 $(1)$

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

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