Question

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

• A. $3$
• B. $-2$
• C. $2$
• D. $-1$

Answer 1

Answer: (D)

$-1$

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