Question

Simplify $\cos {12}^{\circ }\cot {38}^{\circ }\cot {52}^{\circ }\cot {60}^{\circ }\cot {78}^{\circ }$

Answer 1

$\cot 12°\cot 38°\cot 52°\cot 60°\cot 78°$

$=\cot (90°-78°)\cot (90°-52°)\cot 52°\cot 60°\cot 78°$

$=\left(\tan 78°\cot 78°\right)\left(\tan 52°\cot 52°\right)\sqrt{3}$

$=\sqrt{3}$

Hence, the answer is $\sqrt{3}$

$PropertyUsed$

$\cot \left({90}^{\circ }-\theta \right)=\tan \theta$

$\tan \theta =\frac{1}{\cot \theta }$