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Question

If in a triangle ABC, C=60o, then 1a+c+1b+c=
[IIT 1975]


A

1a+b+c

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B

2a+b+c

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C

3a+b+c

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D

None of these

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Solution

The correct option is C

3a+b+c


cos C=π3a2+b2c2=ab
b2+bc+a2+ac=ab+ac+bc+c2
b(b+c)+a(a+c)=(a+c)(b+c)
Divide by (a+c)(b+c) and add 2 on both sides
1+ba+c+1+ab+c=3 1a+c+1b+c=3a+b+c.


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