If alpha, beta and gamma are the angles made | vedclass

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(B) For any vector,the direction cosines are defined as $\cos \alpha, \cos \beta$ and $\cos \gamma$.We know the fundamental identity for direction cos

Vedclass · Accepted Answer

$1 + \cos ^2 \gamma$

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(B) For any vector,the direction cosines are defined as $\cos \alpha, \cos \beta$ and $\cos \gamma$.We know the fundamental identity for direction cosines is $\cos ^2 \alpha + \cos ^2 \beta + \cos ^2 \gamma = 1$.Using the trigonometric identity $\sin ^2 	heta = 1 - \cos ^2 	heta$,we can rewrite the expression as:$(1 - \sin ^2 \alpha) + (1 - \sin ^2 \beta) + (1 - \sin ^2 \gamma) = 1$.$3 - (\sin ^2 \alpha + \sin ^2 \beta + \sin ^2 \gamma) = 1$.$\sin ^2 \alpha + \sin ^2 \beta + \sin ^2 \gamma = 2$.Therefore,$\sin ^2 \alpha + \sin ^2 \beta = 2 - \sin ^2 \gamma$.Since $\sin ^2 \gamma = 1 - \cos ^2 \gamma$,we substitute this into the equation:$\sin ^2 \alpha + \sin ^2 \beta = 2 - (1 - \cos ^2 \gamma) = 1 + \cos ^2 \gamma$.

If $\alpha, \beta$ and $\gamma$ are the angles made by a vector with $x, y$ and $z$ axes respectively,then $\sin ^2 \alpha + \sin ^2 \beta =$

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