If a,b,c are in A.P, then prove that: `2sinA/2.sinC/2=sinB/2`

1.	If a,b,c are in A.P, then prove that: `2sinA/2.sinC/2=sinB/2`
Answer» Let `2sinA/2.sinC/2=sinB/2` `rArr 2sqrt((s-b)(s-c))/(bc).sqrt((s-a)(s-b))/(ab)=sqrt((s-a)(s-c))/(ac)` `rArr 2(s-b)/b.sqrt((s-a)(s-c))/(ac)=sqrt((s-a)(s-c))/(ac)` `rArr 2(s-b)/(b)=1` `rArr 2s-2b=b` `rArr a+b+c-2b=b` `rArr a+c=2b` `rArr a+c=2b` `rArr` a,b,c are in A.P. Which is given. Therefore, `2sinA/2.sinC/2=sinB/2`, if a,b,c are in A.P. Hence proved.

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