Question

If the angles made by a straight line with the coordinate axes are $\alpha ,\frac{\pi }{2}-\alpha ,\beta ,\text{then}\beta =$

• A. $0$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

The correct option is C $\frac{\pi }{2}$

${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$
Given: $\alpha =\alpha ,\beta =\frac{\pi }{2}-\alpha ,\gamma =\beta$
${\cos }^2\alpha +{\sin }^2\alpha +{\cos }^2\beta =1\Rightarrow 1+{\cos }^2\beta =1\Rightarrow {\cos }^2\beta =0\Rightarrow \cos \beta =0\Rightarrow \beta =\frac{\pi }{2}$