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iit jee Grade: 12
        

let 1< m<3. In a triangle ABC if 2b = (m+1)a and


cos A = [(m-1)(m+3)/4m]1/2 . prove that there r 2 values for the third side one of which is m times the other.

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear


cos A = [(m-1)(m+3)/4m]1/2


calculate sinA = [1-cos2A]1/2


                    = [(m+1)(3-m)/4m]1/2


 


now sinB /b =sinA /a


sinB = (m+1)/2 sinA


         =  [(m+1)3(3-m)/16m]1/2


 


now calculate CosB = ± [1-sin2B]1/2


                                    =± [(m-1)3(m+3)/16m]1/2


now sinC =sin(180 -A-B)


                 =sin(A+B)


                 =sinA cosB + cosA sinB


 


                 =[(m-1)(m+3)(1+m)(3-m)/16m2]1/2 [(1+m) ±(m-1)]


 


 


for + value   SinC =[(m-1)(m+3)(1+m)(3-m)/16m2]1/2 [2m]


for - alue     sinC =[(m-1)(m+3)(1+m)(3-m)/16m2]1/2 [(2]


 


clearly one value is m times the other


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Badiuddin

7 years ago
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