If a straight line is equally inclined at an angle $ heta$ with all the three coordinate axes, then $ an heta=$

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If a straight line is equally inclined at an angle $	heta$ with all the three coordinate axes, then $	an 	heta=$

Aicharya · Accepted Answer

Since the line is making equal angle $	heta$ with the 3 co-ordinate axes. Hence $\alpha=\beta=\gamma=	heta$ $ 	herefore l=m=n=\cos 	heta $ We know that, $l^2+m^2+n^2=1$ $ \begin{aligned} & \Rightarrow 3 l^2=1 \Rightarrow l=\frac{1}{\sqrt{3}} \ & \Rightarrow \cos 	heta=\frac{1}{\sqrt{3}} \Rightarrow \sin 	heta=\frac{\sqrt{2}}{\sqrt{3}} \end{aligned} $ Hence $	an 	heta=\frac{\sin 	heta}{\cos 	heta}=\sqrt{2}$

If a straight line is equally inclined at an angle $\theta$ with all the three coordinate axes, then $\tan…

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