The solution set of the equation tan(pi tan x | vedclass

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Question

(A) Given the equation $	an(\pi 	an x) = \cot(\pi \cot x)$.Using the identity $\cot 	heta = 	an(\frac{\pi}{2} - 	heta)$,we have $	an(\pi 	an x)

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$\phi$

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(A) Given the equation $	an(\pi 	an x) = \cot(\pi \cot x)$.Using the identity $\cot 	heta = 	an(\frac{\pi}{2} - 	heta)$,we have $	an(\pi 	an x) = 	an(\frac{\pi}{2} - \pi \cot x)$.This implies $\pi 	an x = n\pi + \frac{\pi}{2} - \pi \cot x$ for some integer $n$.For the simplest case $n=0$,we get $	an x + \cot x = \frac{1}{2}$.Substituting $\cot x = \frac{1}{	an x}$,we get $	an x + \frac{1}{	an x} = \frac{1}{2}$.Multiplying by $	an x$,we obtain $2 	an^2 x - 	an x + 2 = 0$.The discriminant $D = (-1)^2 - 4(2)(2) = 1 - 16 = -15$.Since $D Thus,the solution set is $\phi$.

The solution set of the equation $\tan(\pi \tan x) = \cot(\pi \cot x)$ is

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