If a vector overrightarrow{P} makes angles al | vedclass

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(C) For any vector,the direction cosines satisfy the relation $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.We know the trigonometric identity $\

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$2$

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(C) For any vector,the direction cosines satisfy the relation $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$.We know the trigonometric identity $\sin^2 	heta = 1 - \cos^2 	heta$.Substituting this into the expression:$\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = (1 - \cos^2 \alpha) + (1 - \cos^2 \beta) + (1 - \cos^2 \gamma)$$= 3 - (\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma)$$= 3 - 1$$= 2$

If a vector $\overrightarrow{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

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