If frac{cos^4 alpha}{cos^2 beta} + frac{sin^4 | vedclass

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(B) Given: $\frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1$. Let $\frac{\cos^2 \alpha}{\cos \beta} = \cos 	heta$ and $\f

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$1$

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(B) Given: $\frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1$. Let $\frac{\cos^2 \alpha}{\cos \beta} = \cos 	heta$ and $\frac{\sin^2 \alpha}{\sin \beta} = \sin 	heta$. Then $\cos^2 \alpha = \cos \beta \cos 	heta$ and $\sin^2 \alpha = \sin \beta \sin 	heta$. Adding these,$\cos^2 \alpha + \sin^2 \alpha = \cos \beta \cos 	heta + \sin \beta \sin 	heta = \cos(\beta - 	heta) = 1$. This implies $\beta = 	heta$. Substituting $	heta = \beta$ back into the expressions,we get $\cos^2 \alpha = \cos^2 \beta$ and $\sin^2 \alpha = \sin^2 \beta$. Therefore,$\frac{\cos^4 \beta}{\cos^2 \alpha} + \frac{\sin^4 \beta}{\sin^2 \alpha} = \frac{\cos^4 \beta}{\cos^2 \beta} + \frac{\sin^4 \beta}{\sin^2 \beta} = \cos^2 \beta + \sin^2 \beta = 1$. The greatest integer value $[1] = 1$.

If $\frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1$,then the value of $\left[ \frac{\cos^4 \beta}{\cos^2 \alpha} + \frac{\sin^4 \beta}{\sin^2 \alpha} \right]$ is (where $[.]$ denotes the greatest integer function).

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