Question

If a line makes angles $\alpha ,\beta ,\gamma$ with the coordinate axes, then the value of $\cos 2\alpha +\cos 2\beta +\cos 2\gamma$ is

• A. $3$
• B. $-2$
• C. $2$
• D. $-1$

Answer 1

The correct option is D $-1$

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