HSC Science (Computer Science) 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 Δ ABC with the usual notations prove that (a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2 - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

Question

In Δ ABC with the usual notations prove that `(a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2`

Solution

LHS= `(a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)`

`=a^2[cos^2(C/2)+sin^2(C/2)]+b^2[cos^2(C/2)+sin^2(C/2)]-2ab[cos^2(C/2)-sin^2(C/2)]`

`=a^2+b^2-a^2-b^2+c^2`

`=c^2`

=RHS

Hence proved

 

Is there an error in this question or solution?

APPEARS IN

 2015-2016 (March) (with solutions)
Question 2.2.1 | 4 marks
Solution for question: In Δ ABC with the usual notations prove that (a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2 concept: null - Solution of a Triangle. For the courses HSC Science (Computer Science), HSC Science (Electronics), HSC Arts, HSC Science (General)
S