Question

in any triangle abc prove that a^2=(b+c)^2 sin^2 a/2+ (b-c)^2 cos^2 a/2​

Answer 1

Answer:

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Step-by-step explanation:

In △ABC(a−b)  

2

cos  

2

 

2

c

​  

+(a+b)  

2

sin  

2

 

2

c

​  

=

 

 

 

 

 

 

Video Explanation

Solution to Question ID 633802

ANSWER

(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