Home
Class 12
MATHS
In a DeltaABC,angleC=60^(@), then (1)/...

In a `DeltaABC,angleC=60^(@)`, then `(1)/(a+b)+(1)/(b+c)` is equal to

A

`(1)/(a+b+c)`

B

`(2)/(a+b+c)`

C

`(3)/(a+b+c)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have , `cosC=(a^(2)+b^(2)-c^(2))/(2ab)`
`rArrcos60^(@)=(a^(2)+b^(2)-c^(2))/(2ab)`
`rArra^(2)+b^(2)-c^(2)=ab`
`rArrb^(2)+bc+a^(2)+ac=ab+ac+bc+c^(2)`
`rArrb(b+c)+(a(a+c)=(a+c)(b+c)` On dividing by (a+c)(b+c) and then add 2 both sides we get
`1+(b)/(a+c)+1+(a)/(b+c)=3`
`rArr(1)/(a+c)+(1)/(b+c)=(3)/(a=b+c)`
Promotional Banner

Similar Questions

Explore conceptually related problems

In DeltaABC," if " angleC=90^(@)," then " (a+c)/(b)+(b+c)/(a) is equal to :

In a DeltaABC,angleC=(pi)/(3),"then "(3)/(a+b+c)-(1)/(a+c)=

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

If a DeltaABC, b=2, C=60^(@), c=sqrt(6) , then a =

If angleA=90^(@) in the DeltaABC , then tan^(-1)((c)/(a+b))+tan^(-1)((b)/(a+c)) is equal to

In DeltaABC , if angleC gt angleB , then

In a DeltaABC,angleC=90^(@) , then the equation whose roots are tan A & tan B is

In a DeltaABC , if a = 4, b = 3 and angleA=60^(@) , then c is a root of the equation

If ( a + b) : ( b + c ) : ( c + a) = 5 : 12 : 11 and a + b + c =28 , then (1)/( a) : (1)/( b) : ( 1)/( c ) is equal to: