Question

Without using trigonometric tables, evaluate :

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

Answer 1

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

$=\left(\cot {12}^o\cot {78}^o\right)\left(\cot {38}^o\cot {52}^o\right)\cot {60}^o$

$=\left(\cot {12}^o\tan {12}^o\right)\left(\cot {38}^o\tan {38}^o\right)\cot {60}^o$

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