1.

If `a,b,c inR` then prove that `sec^2theta=(bc+ca+ab)/(a^2+b^2+c^2)`only if a = b = c.

Answer» We know that `sec^2thetage1`
`:. (bc+ca+ab)/(a^2+b^2+c^2)ge 1`
`rArr bc+ca+abgea^2+b^2+c^2`
`rArra^2+b^2+c^2-ab-bc-cale0`
`rArr(a-b)^2+(b-c)^2+(c-a)^2le0`
`rArra-b=0,b-c=0" and "c-a=0`
`rArra=b=c`


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