Question

Solve:
$\cot {12}^o.\cot {38}^o.\cot {52}^o.\cot {60}^o.\cot {78}^o$

Answer 1

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

$=(\cot 12°\cdot \cot 78°)\cdot (\cot 38°\cdot \cot 52°)\cdot \cot 60°$

$=(\cot 12°\cdot \cot (90°-12°))\cdot (\cot 38°\cdot \cot (90°-38°))\cdot \cot 60°$

$=(\cot 12°\cdot \tan 12°)\cdot (\cot 38°\cdot \tan 38°)\cdot \cot 60°$

$=1\times 1\times \frac{1}{\sqrt{3}}$

$=\frac{1}{\sqrt{3}}$