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 $\fr

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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 $\beta = 	heta + 2n\pi$,so $\cos \beta = \cos 	heta$ and $\sin \beta = \sin 	heta$.Substituting back,$\cos^2 \alpha = \cos^2 \beta$ 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 of $1$ is $[1] = 1$.

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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