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If sin(x+y)/sin(x-y)=a+b/a-b ,then tan(x)/tan(y)

If sin(x+y)/sin(x-y)=a+b/a-b ,then tan(x)/tan(y)

Grade:11

4 Answers

AKASH GOYAL AskiitiansExpert-IITD
420 Points
13 years ago

Dear Hemanth

LHS = sin(x+y)/sin(x-y)

      = (sinx*cosy + cosx*siny) / (sinx*cosy - cosx*siny)

comparing LHS with RHS

a=sinx*cosy

b=cosx*siny

divide a by b

a/b= tanx/tany

 

All the best

AKASH GOYAL
AskiitiansExpert-IITD

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Devasish Bindani
45 Points
13 years ago

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yo man dont think i had this pic in my pc i made this pic just to answer your querry

Souradeep Majumder
80 Points
13 years ago

DO COMPONENDO DIVIDENDO AND THE USE THE FORMULA sinc+sind and SINC-SIND.........  YOU WILL GET YOUR ANSWER.............

 

APPROVE MY ANSWER...............

Prapti
13 Points
4 years ago
Sin(x+y)            a+b
_________=      ________
Sin(x-y)             a-b
 
=  sin(x+y)+sin(x-y)          (a+b)+(a-b)
 
______________________=______________
Sin(x+y)-sin(x-y)                (a+b)-a+b
 
=    by using identity[2sinAcosB=sin(a+b)+sin(a-b)
 
=   2 sin x cos y          2a
        ______________=    ______
         2 cos x sin y          2b
 
  =  as we know[ sin x ÷ cos x =tan x]
SO =  tan x  ×  1         a
                      ____=     ___
 
                       tan y       b
 
Therfore tan x          a
                 ______ = _____      hence proved
                 tan y          b
 

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