If frac{cos alpha}{sin beta} = n and frac{cos | vedclass

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(C) Given:$n = \frac{\cos \alpha}{\sin \beta} \implies \cos \alpha = n \sin \beta \quad (1)$$m = \frac{\cos \alpha}{\cos \beta} \implies \cos \alpha =

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$\frac{n^2}{m^2 + n^2}$

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(C) Given:$n = \frac{\cos \alpha}{\sin \beta} \implies \cos \alpha = n \sin \beta \quad (1)$$m = \frac{\cos \alpha}{\cos \beta} \implies \cos \alpha = m \cos \beta \quad (2)$Equating $(1)$ and $(2)$:$n \sin \beta = m \cos \beta$Squaring both sides:$n^2 \sin^2 \beta = m^2 \cos^2 \beta$Using the identity $\sin^2 \beta = 1 - \cos^2 \beta$:$n^2 (1 - \cos^2 \beta) = m^2 \cos^2 \beta$$n^2 - n^2 \cos^2 \beta = m^2 \cos^2 \beta$$n^2 = (m^2 + n^2) \cos^2 \beta$Therefore,$\cos^2 \beta = \frac{n^2}{m^2 + n^2}$.

If $\frac{\cos \alpha}{\sin \beta} = n$ and $\frac{\cos \alpha}{\cos \beta} = m$,then the value of $\cos^2 \beta$ is:

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