In ΔABC,ifsinA:sinC=sin(A−B):sin(B−C), then

a, b, care in A.P.

a2, b2, c2are in A.P.

a2, b2, c2are in G. P.

None of these

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Benjamin Discussed

In ΔABC,ifsinA:sinC=sin(A−B):sin(B−C), then

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Text solutionVerified

sinAsinC=sin(A−B)sin(B−C) ⇒ sin(B+C)sin(B−C)=sin(A+B)sin(A−B) ⇒ sin2B−sin2C=sin2A−sin2B ⇒ 2sin2B=sin2A+sin2C⇒2b2=a2+c2 Hence a2,b2,c2 are in A.P.

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Question Text	In ΔABC,ifsinA:sinC=sin(A−B):sin(B−C), then
Answer Type	Text solution:1
Upvotes	150