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`

Options

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

Answer

B

Explanation

`(sinA)/(c sin B) + (sin B)/(c) + (sin C)/(b) = (c)/(ab) + (b)/(ac) + (a)/(bc)`
or `(a)/(bc) + (sinB)/(c) + (sin C)/(b) = (c)/(ab) + (b)/(ab) + (a)/(bc)`
or `(sin B)/(c) + (sin C)/(b) = (c)/(ab) + (b)/(ac)`
or `(b sin B + c sin C)/(bc) = (c^(2) + b^(2))/(abc)`
or `a = (b^(2) + c^(2))/(b sin B + c sin C)`
`= (b (2R sin B) + c(2R sin C))/(b sin B + c sin C)`
`= 2R`
`rArr angleA = (pi)/(2)`