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 (a)`120^0` (b) `90^0` (c) `60^0` (d) `30^0`

Options

A. `120^(@)`
B. `90^(@)`
C. `60^(@)`
D. `30^(@)`

Explanation

We have
`(sinA)/(csinB)+(sinB)/c+(sinC)/b=c/(ab)+b/(ac)+a/(bc)`
`rArr(ka)/(kbc)+(bsinB+csinC)/(bc)=(c^(2)+b^(2))/(abc)`
`rArr(bsinB+csinC)/(bc)=(c^(2)+b^(2))/(abc)`
`rArra=(b^(2)+c^(2))/(bsinB+csinC)`
`rArra=(2bRsinB+2cRsinC)/(bsinB+csinC)[becausea/(sinA)=b/(sinB)=c/(sinC)=2R]`
`rArra=2R`
`rArr2RsinA=2RrArrsinA=1rArrA=90^(@)`