If C=60° then show that a÷b+c + b÷c+a =1​

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If C=60° then show that a÷b+c + b÷c+a =1​

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Arya 1 month 2021-08-17T21:24:28+00:00 2 Answers 0 views 0

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    0
    2021-08-17T21:26:12+00:00

    Hy I will help you...

    => 1/(a+c) + 1/(b+c) = 3 / ( a+b+c )

    => (a+b+2c) / (a+c) (b+c) = 3 / (a+b+c) =>(a+b+2c) (a+b+c) = 3(a+c) (b+c)

    => a^2 + b^2 + 2ab + 2c^2 + 3ac + 3bc = 3ab + 3ac + 3bc + 3c^2

    => a^2 + b^2 + 2ab – 3ab = 3 c^2 – 2 c^2 (cancel 3ac & 3bc)

    => a^2 + b^2 – ab = c^2

    0
    2021-08-17T21:26:27+00:00

    Step-by-step explanation:

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    MATHS

    If in a triangle ABC,∠C=60

    , then prove that

    a+c

    1

    +

    b+c

    1

    =

    a+b+c

    3

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    ANSWER

    Formula:

    c

    2

    =a

    +

    b

    2

    −2abcosC

    Given, ∠C=60

    ∴c

    2

    =a

    +

    b

    2

    −2abcos60

    c

    2

    =a

    +

    b

    2

    −ab…………..(1)

    To prove:

    a+c

    1

    +

    b+c

    1

    =

    a+b+c

    3

    a+c

    1

    +

    b+c

    1

    =

    a+b+c

    3

    (a+c)(b+c)

    a+b+2c

    =

    a+b+c

    3

    (a+b+2c)(a+b+c)=3[(a+c)(b+c)]

    a

    2

    +ab+ac+ba+b

    2

    +bc+2ca+2cb+2c

    2

    =3ab+3ac+3cb+3c

    2

    a

    2

    +b

    2

    +2ab−3ab=3c

    2

    −2c

    2

    a

    2

    +b

    2

    −ab=c

    2

    ………….(2)

    From (1) and (2) it’s clear that,

    a+c

    1

    +

    b+c

    1

    =

    a+b+c

    3

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