Question

please solve this
any one who are genius​

Answer 1

Given

$\rm cot\dfrac{\pi}{24}.cot\dfrac{3\pi}{24}.cot\dfrac{5\pi}{24}.cot\dfrac{7\pi}{24}.cot\dfrac{9\pi}{24}.cot\dfrac{11\pi}{24}$

To Find

Value of the given data

Formula Applied

$\bullet\ \; \rm cot(90-\theta )=tan\theta\\\\\bullet\ \; \rm tan\theta .cot\theta=1$

Solution

$\bf cot\dfrac{\pi}{24}\\\\\to \rm tan \left(\dfrac{\pi}{2}-\dfrac{\pi}{24}\right)\\\\\to \bf \blue{tan\dfrac{11\pi}{24}}$

$\bf cot\dfrac{3\pi}{24}\\\\\to \rm tan\left(\dfrac{\pi}{2}-\dfrac{3\pi}{24}\right)\\\\\to \bf \blue{tan\dfrac{9\pi}{24}}$

$\bf cot\dfrac{5\pi}{24}\\\\\to \rm tan\left( \dfrac{\pi}{2}-\dfrac{5\pi}{24}\right)\\\\\to \bf \blue{tan\dfrac{7\pi}{24}}$

Now , sub. these values in the given data ,

$\to \rm cot\dfrac{\pi}{24}.cot\dfrac{3\pi}{24}.cot\dfrac{5\pi}{24}.cot\dfrac{7\pi}{24}.cot\dfrac{9\pi}{24}.cot\dfrac{11\pi}{24}\\\\\to \rm \left(tan\dfrac{11\pi}{24}\right).\left(tan\dfrac{9\pi}{24}\right).\left(tan\dfrac{7\pi}{24}\right).cot\dfrac{7\pi}{24}.cot \dfrac{9\pi}{24}.cot\dfrac{11\pi}{24}\\\\\to \bf \pink{1\ \; \bigstar}$

So , Option (1) is correct