If `cosalpha+cosbeta+cosgamma=0,"where "0ltalphale(pi)/(2),0ltbetale(pi)/(2),0ltgammale(pi)/(2)`, then what is the value of sin ` alpha+sinbeta+singamma`?

Options

A. 0
B. 3
C. `(5sqrt(2))/(2)`
D. `(3sqrt(2))/(2)`

Answer

B

Explanation

`cosalpha+cosbeta+cosgamma=0` . . . (1)
Given , `0ltalphale(pi)/(2),0ltbetale(pi)/(2),0ltgammale(pi)/(2)`.
(1) is satisfied when `alpha=(pi)/(2),beta=(pi)/(2)andgamma=(pi)/(2)`.
`thereforesinalpha+sinbeta+singamma="sin"(pi)/(2)+"sin"(pi)/(2)+"sin"(pi)/(2)`.
`=1+1+1=3`.