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In a A B C ,if|(1 ,1 ,1),( 1+cosA,1+cos...

In a ` A B C ,if|(1 ,1 ,1),( 1+cosA,1+cosB,1+cosC),(cos^2A+cosB,cos^2A+cosB,cos^2+cosC)|=0` show that ` A B C` is an isosceles.

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Given,
`|(1 ,1 ,1),( 1+cosA,1+cosB,1+cosC),(cos^2A+cosB,cos^2A+cosB,cos^2+cosC)|=0`
Applying `C_2​->C_2​−C_3​ and C_3​->C_3​−C_2`
​`|(1 ,1 ,1),( 1+cosA,cosB-cosC,cosC-cosB),(cos^2A+cosB,cosB-cosC,cosC-cosB)|=0`
=`1[(cosB−cosC)(cosC−cosB)−(cosB−cosC)(cosC−cosB)]=0`
=`cosB−cosC=0`
...
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