Home
Class 12
MATHS
In a triangle ABC if cot(A/2)cot(B/2)=c,...

In a triangle `ABC` if `cot(A/2)cot(B/2)=c, cot(B/2)cot(C/2)=a ` and `cot(C/2)cot(A/2)=b` then `1/(s-a)+1/(s-b)+1/(s-c)=`

A

`-1`

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
`cot.(A)/(2)cot.(B)/(2)=sqrt((s(s-a))/((s-b)(s-c))xx(s(s-b))/((s-c)(s-a)))=c`
`rArr (s)/(s-c)=c rArr (1)/(s-c)=(c )/(s)`
Similarly `(1)/(s-a)=(a)/(s),(1)/(s-b)=(b)/(s)`
`rArr (1)/(s-a)+(1)/(s-b)+(1)/(s-c)=(a+b+c)/(s)=(2s)/(s)=2`
Promotional Banner

Topper's Solved these Questions

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Multiple Correct Answers Type|13 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Comprehension Type|6 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|15 Videos

  • STATISTICS

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC, if r^(2)cot((A)/(2))cot((B)/(2))cot((C)/(2))=

In any triangle ABC prove that cot(A/2)+cot(B/2)+cot(C/2)=cot(A/2)cot(B/2)cot(C/2)

In a triangle ABC,if a cot A+b cot B+c cot C=

cot((A)/(2))+cot((B)/(2))+cot((C)/(2))=

If in a triangle ABC ,b +c=4a then cot(B/2)cot(C/2) is equal to

If A+B+C=pi , prove that : cot( A/2)+ cot(B/2) + cot( C/2) = cot( A/2) cot(B/2) cot(C/2)

In /_\ ABC, if 2b=a+c then cot(A/2)cot(C/2)=

In triangle ABC, if |[1,1,1], [cot (A/2), cot(B/2), cot(C/2)], [tan(B/2)+tan(C/2), tan(C/2)+ tan(A/2), tan(A/2)+ tan(B/2)]| then the triangle must be (A) Equilateral (B) Isoceless (C) Right Angle (D) none of these

In any !ABC ,If cot(A/2),cot(B/2),cot(C/2) are in A.P.,then a,b,c are in

In any Delta ABC,cot((A)/(2)),cot((B)/(2)),cot((C)/(2)) are in A.P.