Home
Class 11
MATHS
In a triangle A B C ,/C=60^0, then prove...

In a triangle `A B C ,/_C=60^0,` then prove that: `1/(a+c)+1/(b+c)=3/(a+b+c)dot`

Text Solution

Verified by Experts

Let `1/(a+b)+1/(b+c)=3/(a+b+c)`
`rArr (b+c+a+b)/((a+b)(b+c))=3/(a+b+c)`
`rArr (a+2b+c)(a+b+c)=3(a+b)(b+c)`
`rArr a^(2)+2b^(2)+c^(2)+3ab+3bc+2ac = 3ab + 3b^(2)+3ac+3bc`
`rArr a^(2)+c^(2)-b^(2)=ac`
`rArr (a^(2)+c^(2)-b^(2))/(2ac)=1/2`
`rArr cosB=cos60^(@)`
`rArr B=60^(2)`
`therefore` In `DeltaABC, angleB=60^(@)`
`rArr 1/(a+b)+1/(b+c)=3/(a+b+c)`. Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3A|11 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3B|22 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN|Exercise Exercise|206 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC,/_C=60^(@), then prove that: (1)/(a+c)+(1)/(b+c)=(3)/(a+b+c).

If in a triangle ABC,/_C=60^(@), then prove that (1)/(a+c)+(1)/(b+c)=(3)/(a+b+c).

If in a triangle ABC,/_C=60^(@), then prove that (1)/(a+c)+(1)/(b+c)=(3)/(a+b+c)

If C=60^(@). then prove that (1)/(a+c)+(1)/(b+c)=(3)/(a+b+c)

If in a triangle ABC, angleC=60^(@) , then (1)/(a+c)+(1)/(b+c)-(3)/(a+b+c) =

If in triangle ABC, C = 90^circ then prove that tan^(-1) (a/(c+b)) + tan^(-1) (b/(a+c)) = pi/4 .

In a triangle ABC, prove that (1+(b-c)/a)^a*(1+(c-a)/b)^b*(1+(a-b)/c)^cle1 .

If, in a triangleABC, A=60^(@) , then: (1+a/c + b/c)(1+c/b - a/b)=

In a triangle ABC prove that a/(a+c)+b/(c+a)+c/(a+b)<2

In any triangle ABC,prove that a sin (B-C)+b sin(C-A)+c sin(A-B)=0