If frac{cos x}{cos (x-2 y)}=lambda,then tan ( | vedclass

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(B) We are given $\lambda = \frac{\cos x}{\cos (x-2 y)}$.Consider the expression $	an (x-y) 	an y = \frac{\sin (x-y) \sin y}{\cos (x-y) \cos y}$.Mul

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$\frac{1-\lambda}{1+\lambda}$

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(B) We are given $\lambda = \frac{\cos x}{\cos (x-2 y)}$.Consider the expression $	an (x-y) 	an y = \frac{\sin (x-y) \sin y}{\cos (x-y) \cos y}$.Multiplying the numerator and denominator by $2$,we get $\frac{2 \sin (x-y) \sin y}{2 \cos (x-y) \cos y}$.Using the product-to-sum formulas $2 \sin A \sin B = \cos(A-B) - \cos(A+B)$ and $2 \cos A \cos B = \cos(A-B) + \cos(A+B)$,we have:$	an (x-y) 	an y = \frac{\cos(x-2y) - \cos x}{\cos(x-2y) + \cos x}$.Dividing the numerator and denominator by $\cos(x-2y)$,we get:$\frac{1 - \frac{\cos x}{\cos(x-2y)}}{1 + \frac{\cos x}{\cos(x-2y)}} = \frac{1-\lambda}{1+\lambda}$.

If $\frac{\cos x}{\cos (x-2 y)}=\lambda$,then $\tan (x-y) \tan y$ is equal to

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