If$\ 4n\alpha = \ \pi,\$then the value of $ an{\alpha \bullet an{2\alpha \bullet an{3\alpha \bullet an\ 4\alpha\ldots an{(2n - 2)\alpha\ }}}} an{(2n - 1)}\alpha$ is

Question

If$\ 4n\alpha = \ \pi,\$then the value of $	an{\alpha \bullet 	an{2\alpha \bullet 	an{3\alpha \bullet 	an\ 4\alpha\ldots	an{(2n - 2)\alpha\ }}}}	an{(2n - 1)}\alpha$ is

Dr. Abubacker · Accepted Answer

(b)
$	an{\alpha	an{2\alpha\ldots	an{(2n - 1)\alpha	an{(2n - 1)\alpha}}}}$
$= \left\{ 	an{\alpha	an{(2n - 1)\alpha}} ight\}\left\{ 	an{2\alpha	an{(2n - 2)\alpha}} ight\}\ldots\left\{ 	an{(n - 1)\alpha	an{(n + 1)\alpha}} ight\}	an{n\alpha}$
$= \left\{ 	an{\alpha	an\left( \frac{\pi}{2} - \alpha ight)} ight\}\left\{ 	an{2\alpha	an\left( \frac{\pi}{2} - 2\alpha ight)} ight\}\ldots	an\frac{\pi}{4}\ \ \left( \because n\alpha = \frac{\pi}{4} ight)$
$= 1$

Q. If$\ 4n\alpha = \ \pi,\$then the value of $\tan{\alpha \bullet \tan{2\alpha \bullet \tan{3\alpha \bullet \tan\ 4\alpha\ldots\tan{(2n - 2)\alpha\ }}}}\tan{(2n - 1)}\alpha$ is

Explanation

Reviewed by Dr. Abubacker

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