The solution set of the equation tan(pi, tanx | vedclass

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Question

$	an (\pi 	an x)=\cot (\pi \cot x)$

$=	an \left(\frac{\pi}{2}-\pi \cot xight)$

$\Rightarrow \quad \pi 	an x=\frac{\pi}{2}-\pi \cot x$

$

Vedclass · Accepted Answer

$\phi $

Vedclass · Answer

$	an (\pi 	an x)=\cot (\pi \cot x)$

$=	an \left(\frac{\pi}{2}-\pi \cot xight)$

$\Rightarrow \quad \pi 	an x=\frac{\pi}{2}-\pi \cot x$

$\Rightarrow \quad 	an x+\cot x=\frac{1}{2}$

$\Rightarrow \quad 	an x+\frac{1}{	an x}=\frac{1}{2}$

$\Rightarrow \quad 2 	an ^{2} x+2=	an x$

$\Rightarrow \quad 2 	an ^{2} x-	an x+2=0$

This is quadratic in $	an \mathrm{x}$.

$\Rightarrow \quad 	an x=\frac{1 \pm \sqrt{1-4.4}}{4}=\frac{1 \pm \sqrt{-15}}{2}$

which are not real

$	herefore $ solution set $=\phi$

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

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