If A +B 225, then show that cot A/1+cot A .cot B/1+cot B =1/2

COTACOTB)/[(1+COTA)(1+COTB)] = 1/2

TAKING LHS

 = (COTACOTB)/[1+COTACOTB +COTA+COTB] ...................1

NOW

COT(A+B)=COTACOTB - 1/COTA+COTB

A+B = 225 (GIVEN)

SO

      COT225 = COTACOTB - 1/COTA+COTB

      1 = COTACOTB-1/COTA+COTB                                                  (COT225=1)

  COTA + COTB =COTACOTB - 1 ......................2

PUTTING 2 IN 1 WE GET

   LHS= COTACOTB/2COTACOTB

        =1/2 = RHS

Regards

Arun (askIITians forum expert)