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

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

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
 

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)

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