Question

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

• A. $1$
• B. $3$
• C. $-1$
• D. $0$

Answer 1

The correct option is C $-1$

${\cos }^2\alpha +{\cos }^2\beta +{\cos }^{2}r=1$

$\cos 2\alpha +{\cos }^2\beta +\cos 2r=2{\cos }^2\alpha -1+2{\cos }^2\beta -1+2{\cos }^{2}r-1$

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

$=2\left(1\right)-3$

$=-1$