Question

In ∆ABC , sin^2(A/2)+sin^2(B/2)+sin^2(C/2) =
​

Answer 1

Answer:

Step-by-step explanation:

(a−b)  

2

cos  

2

 

2

C

​  

+(a+b)  

2

sin  

2

 

2

C

​  

 

=a  

2

+b  

2

+2ab(sin  

2

 

2

C

​  

−cos  

2

 

2

C

​  

)

=a  

2

+b  

2

+2ab(2sin  

2

 

2

C

​  

−1)

But sin  

2

C

​  

=  

ab

(s−a)(s−b)

​  

 

​  

 

where s=  

2

a+b+c

​  

 

∴

a  

2

+b  

2

+2ab(2sin  

2

 

2

C

​  

−1)

=a  

2

+b  

2

+2ab(  

2ab

(c+b−a)(c+a−b)

​  

−1)

=a  

2

+b  

2

+c  

2

−(b−a)  

2

−2ab

=c  

2