Question

cot 12 cot 38 cot 52 cot 60 cot 78

Answer 1

$$\begin{gathered} \cot 12\times \cot 38\times \cot 52\times \cot 60\times \cot 78 \\ =\cot \left(90-78\right)\times \cot \left(90-52\right)\times \cot 52\times \frac{1}{\sqrt{3}}\times \cot 78 \\ =\tan 78\times \tan 52\times \cot 52\times \cot 78\times \frac{1}{\sqrt{3}} \\ =\tan 78\times \cot 78\times \tan 52\times \cot 52\times \frac{1}{\sqrt{3}} \\ =1\times 1\times \frac{1}{\sqrt{3}} \\ =\frac{1}{\sqrt{3}} \end{gathered}$$