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Show that (cosA)/(a)+(cosB)/(b)+(cosC)/(...

Show that `(cosA)/(a)+(cosB)/(b)+(cosC)/(c)=(a^(2)+b^(2)+c^(2))/(2abc)`

Text Solution

Verified by Experts

The correct Answer is:
`(a^(2)+b^(2)+c^(2))/(2abc)=R.H.S`
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Knowledge Check

  • If in a triangle ABC,(1+cosA)/(a)+(1+cosB)/(b)+(1+cosC)/(c)=(k^(2)(1+cosA)(1+cosB)(1+cosC))/(abc) then k is equal to

    A
    `(1)/(2 sqrt(2)R`
    B
    2R
    C
    `(2)/(R)`
    D
    None of these

  • In a triangleABC, " if "(cosA)/(a)= (cosB)/(b)=(cosC)/(c ) then triangleABC is

    A
    Right angled
    B
    Isosceles right angled
    C
    Equilateral
    D
    Scalene

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    Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-b)(b-c)(c-a)

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    Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}|=(a^(3)+b^(3)+c^(3)-3abc)^(2)

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