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In DeltaABC if sinA.sin(B-C)= sinC.sin(A...

In `DeltaABC` if sinA.sin(B-C)= sinC.sin(A-B),then-`(A!=B!=C)` (A) tanA, tanB, tanC are in arithmetic progression (B) cotA, cotB, cotC are in arithmetic progression (C) cos2A, cos2B, cos2C are in arithmetic progression (D) sin2A. sin2B. sin2C are in arithmetic progression

Text Solution

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A+B+C=180
A=180-(B+C)
C=180-(A+B)
sin(180-(B+C))sin(B_C)=sin(180-(A+B)sin(A-B)
sin(B+C)sin(B-C)=sin(A+B)sin(A-B)
`2sin^B-2sin^2C=2sin^2A-2sin^2B`
`4sin^2B-2=2sin^2A+2sin^2C-2`
`2sin^(-2)B-1+2sin^(-2)B-1=2sin^(-2)A-1+2sin^(-2)C-1 `
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