Question

A line makes angles $\alpha$, $\beta$, $\gamma$ with the positive directions of the axes of reference. The value of $\cos 2\alpha +\cos 2\beta +\cos 2\gamma$ is

• A. $1$
• B. $2$
• C. $-1$
• D. $0$

Answer 1

The correct option is C $-1$

The value of $\cos 2\alpha +\cos 2\beta +\cos 2\gamma$

$=(1+\cos 2\alpha +1+\cos 2\beta +1+\cos 2\gamma )-3$

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

$=2-3$

$=-1$