let 1&lt; m&lt;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.

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.

8 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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