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In Delta ABC , If b/(c^2-a^2)+a/(c^2-b...

In `Delta ABC , If b/(c^2-a^2)+a/(c^2-b^2)=0` then

A

`(pi)/(2)`

B

`(pi)/(4)`

C

`(2pi)/(3)`

D

`(pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)=k("say")`
`therefore (a)/(b^(2)-c^(2))+(c)/(b^(2)-a^(2))=0`
`implies (k sinA)/(k^(2)(sin^(2)B-sin^(2)c))+(k sinC)/(k^(2)(sin^(2)B-sin^(2)A))=0`
`implies (sinA)/(sin(B+C)sin(B-C))+(sinC)/(sin(B+A)sin(B-A))=0`
`implies(sinA)/(sin(B+C)sin(B-C))+(sinC)/(sin(B+A)sin(B-A))=0`
`implies(1)/(sin(B-C))+(1)/(sin(B-A))=0`
`impliessin(B-A)+sin(B-C)=0`
`impliessin(A-B)=sin(B-C)`
`impliesA-B=B-CimpliesA+C=2BimpliesB=60^(@)`
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