Question

If $\alpha ,\beta$ and $\gamma$ are the angles which a half ray makes with the positive direction of the axes, then ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$ is equal to

• A. $1$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

Answer: (B)

$2$

Given expression, ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma$
$=(1-{\cos }^2\alpha )+(1-{\cos }^2\beta )+(1-{\cos }^2\gamma )$
$=3-{\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =3-1=2$
$(\because {\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1)$