MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 11
        if tanA/2,tanB/2,tanC/2 are in harmonic progression then find value of cotB/2
8 years ago

Answers : (3)

SAGAR SINGH - IIT DELHI
879 Points
							

Dear student,

Use the concept:

tan (A + B + C) =

=

=

So, since tan (A + B + C) = tan (1800) = 0

So, tanA + tanB + tanC - tanA + tanB + tanC = 0

=> tanA + tanB + tanC = tanA + tanB + tanC.
(vi) cotA + cotB + cotA + cotC + cotB cotC = 1
(vii)
(viii)

8 years ago
vikas askiitian expert
509 Points
							

tanA/2 , tanB/2 , tanC/2 are in HP so

 

2/tanB/2 = 1/tanA/2 + 1/tanC/2

2/tanB/2 = (tanA/2 + tanB/2)/tanA/2tanB/2            .....................1

 

cotB/2 =cot[pi/2-(A+C)/2]                                      { B/2 = pi/2 - (A+C/2) }

         = tan(A/2+C/2) = tan(A/2)+tan(C/2)/1-tan(A/2)tan(C/2)

 

from this eq value of tanA/2 + tanB/2 = cotB/2 [ 1-tanA/2tanC/2 ]        ....................2

plugging this in eq 1 we get

 

2/tanB/2 = cotB/2 [ 1-tanA/2tanC/2 ]/tanA/2tanC/2

tanA/2tanC/2 = 1/3

now using tangent formulas

this expression simplifies to

a+c = 2b

a,b,c are in Ap

now , cot B/2 can be calulated easily by using

cotB/2 = { s(s-b)/(s-a)(s-c) }1/2

 

approve if u like my ans

8 years ago
Karmanjyot
11 Points
							Let TanA/2 =a TanB/2=bTanC/2=C2/b=1/a+1/C ............(1)A + B +C = 180A/2 +B/2 +C/2 =90ORTan(A/2+C/2)=cotB/2=1/b.....(2)From solving (1) & (2) we get TanA/2 ×TanC/2 =1÷3 From 1 we have a+c=2/3b......(3)Applying A.M.>=G.Ma+c /2>=root(ac)Solving we get 1/b or CotB/2>=root(3)Hence min. Cot B/2= root(3)
						
one year ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details