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paradox xyz cool Grade: 11
        

if   A + B =225


prove that


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


 


 


 


 





6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

(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

6 years ago
sumanth
32 Points
										
 

(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

one year ago
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