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if A + B =225 prove that (cotA.cotB)/[(1 + cotA)(1 + cotB)] = 1/2

if   A + B =225


prove that


(cotA.cotB)/[(1 + cotA)(1 + cotB)] = 1/2


 


 


 


 





Grade:11

2 Answers

vikas askiitian expert
509 Points
11 years ago

(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

HENCE PROVED

sumanth
32 Points
6 years ago
 

(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

 

HENCE PROVED

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