In ΔABC,ifsinA:sinC=sin(A−B):sin(B−C), then  | Filo
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Class 12

Math

Trigonometry

Trigonometric Functions

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

  1. a, b, care in A.P.
  2. a2, b2, c2are in A.P.
  3. a2, b2, c2are in G. P.
  4. None of these
Correct Answer: Option(b)
Solution: 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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