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In any DeltaA B C ,suma(sinB-sin C)= ...

In any ` DeltaA B C ,suma(sinB-sin C)=` `a^2+b^2+c^2` (b) `a^2` (c) `b^2` (d) `0`

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Given,L.H.S=`suma(sinB-sin C)`
=`a(sinB-sin C)+b(sinC-sinA)+c(sinA-sinB)`
By sin rule` [sinA/a=sinB/b=sinC/c=k]`
`suma(sinB-sin C)=a(bk-ck)+b(ck-ak)+c(ak-bk)`
`suma(sinB-sin C)=abk-ack+bck-bak+cak-cbk`
`=suma(sinB-sin C)=0=R.H.S`
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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
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  20. a^2(cos^2B-cos^2C)+b^2(cos^2C-cos^2A)+c^2(cos^2A-cos^2B)=0 .

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