Question

The value of $\cot {12}^{\circ }.\cot {38}^{\circ }.\cot {52}^{\circ }.\cot {60}^{\circ }.\cot {78}^{\circ }$ is:

• A. 1
• B. 0
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D

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

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

= $\cot {12}^{\circ }.\cot {38}^{\circ }.\tan {38}^{\circ }.\frac{1}{\sqrt{3}}.\tan {12}^{\circ }$

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