If `sin^2theta_1+sin^2theta_2+sin^2theta_3=0,` then which of the following is not the possible value of `costheta_1+costheta_2+costheta_3?` (a) `3` (b) `-3` (c) `-1` (d) `-2`

Options

A. 3
B. -3
C. -1
D. -2

Explanation

`sin^2theta_1+sin^2theta_2+sin^2theta_3=0`
`rArr sin^2theta_1=sin^2theta_2=sin^2theta_3=0`
`rArr cos^2theta_1,cos^2theta_2,cos^2theta_3=1`
`rArr costheta_1,costheta_2,costheta_3=pm1`
`cos^2theta_1+cos^2theta_2+cos^2theta_3"can be-3 (when all are -I)"`
or 3 (when all are +I)
or -1 (when any two are -1 and one is +1)
or 1 (when any two are +11 and one is -1)
but-2 is not a possible value.