HSC Science (General) 12th Board ExamMaharashtra State Board
Account
It's free!

User


Login
Create free account


      Forgot password?
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution - In ΔABC, prove that : tan((a-b)/2)=(a-b)/(a+b) cotC/2 - HSC Science (General) 12th Board Exam - Mathematics and Statistics

Question

In ΔABC, prove that : `tan((a-b)/2)=(a-b)/(a+b)cotC/2`

 

 

Solution

In ΔABC by sine rule, we have

`a/sinA=b/sinB=c/sinC=k`

a=ksinA,b=ksinB and c=ksinC

Now, consider

`(a-b)/(a+b)=(ksinA-ksinB)/(ksinA+ksinB)`

`=(sinA-sinB)/(sinA+sinB)`

`=(2cos((A+B)/2).sin((A-B)/2))/(2sin((A+B)/2).cos((A-B)/2))`

`=cot((A+B)/2).tan((A-B)/2)`

`=cot(pi/2-C/2).tan((A-B)/2) .....[because A+B+C=pi]`

`=tan(C/2)tan((A-B)/2)`

`(a-b)/(a+b)=tan((A-B)/2)/cot(C/2)`

`tan((A-B)/2)=(a-b)/(a+b)cot(C/2)`

  Is there an error in this question or solution?

APPEARS IN

Solution for question: In ΔABC, prove that : tan((a-b)/2)=(a-b)/(a+b) cotC/2 concept: null - Solution of a Triangle. For the courses HSC Science (General) , HSC Arts, HSC Science (Electronics), HSC Science (Computer Science)
S