Question

In ` A B C ,` if `(sinA)/(csinB)+(sinB)/c+(sinC)/b=c/(a b)+b/(a c)+a/(b c),` then the value of angle `A` is `120^0` (b) `90^0` (c) `60^0` (d) `30^0`

Answer 1

`sinA/(csinB)+(sinB)/C+sinC/b=c/(ab)+b/(ac)+a/(bc)`
Sine law
`sinA/a=sinB/b=sinC/a=k`
`SinA=ak`
`SinB=bk`
`SinC=ck`
`(ak)/(cbk)+(bk)/(c)+(ck)/b=c/(ab)+b/(ac)+a/(bc)`
`k[b/c+c/b]=1/a[c/b+b/c]`
`k=1/a`
`sinA=ak`
`sinA=a*1/a`
`SinA=1`
`A=90`.