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If the sides a , b and c of A B C are in...

If the sides `a , b and c of A B C` are in `AdotPdot,` prove that `2sinA/2sinC/2=sinB/2`

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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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