Question

15. a. In triangle ABC , show that sin * B/2 = sqrt(((s - a)(s - c))/(ac))​

Answer 1

Answer:

Step-by-step explanation:

Given a+b+c=2s

a+b=2s−c

a+c=2s−b

We know that

cosA=  

2bc

b  

2

+c  

2

−2a  

2

 

​

 

2sin  

2

(  

2

A

​

)=1−cosA

=1−(  

2bc

b  

2

+c  

2

−a  

2

 

​

)

=  

2bc

a  

2

+2bc−(b  

2

+c  

2

)

​

 

2bc

a  

2

−(b  

2

+c  

2

−2bc)

​

 

=  

2bc

a  

2

−(b−c)  

2

 

​

 

=  

2bc

(a+b−c)(a−b+c)

​

 

=  

2bc

(2s−c−c)(2s−b−b)

​

 

=  

2bc

2(s−c)2(s−b)

​

 

bc

2(s−b)(s−c)

​

 

2sin  

2

 

2

A

​

=2.  

bc

(s−b)(s−c)

​

 

2sin  

2

 

2

A

​

=  

bc

(s−b)(s−c)

​

 

sin(  

2

A

​

)=  

bc

(s−b)(s−c)

​

 

​

 

Hence proved