Question

If a line in the space makes angles $\alpha ,\beta$ and $\gamma$ with the coordinate axes, then $\cos 2\alpha +\cos 2\beta +\cos 2\gamma +{\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma =$

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is C $1$

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