If a line makes angles alpha, beta, gamma wit | vedclass

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(B) We know that for a line making angles $\alpha, \beta, \gamma$ with the coordinate axes,the direction cosines are $\cos \alpha, \cos \beta, \cos \g

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$-1$

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(B) We know that for a line making angles $\alpha, \beta, \gamma$ with the coordinate axes,the direction cosines are $\cos \alpha, \cos \beta, \cos \gamma$. It is a known property that $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. Now,we use the identity $\cos 2	heta = 2 \cos^2 	heta - 1$. Substituting this into the expression: $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = (2 \cos^2 \alpha - 1) + (2 \cos^2 \beta - 1) + (2 \cos^2 \gamma - 1)$ $= 2(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) - 3$ $= 2(1) - 3$ $= 2 - 3 = -1$.

If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes in three-dimensional space,then find the value of $\cos 2\alpha + \cos 2\beta + \cos 2\gamma$.

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