Question

Prove that:

cot12° cot38° cot52° cot60° cot78° = \[\frac{1}{\sqrt{3}}\]

Answer 1

\[\left( ii \right) LHS = \cot12° \cot38°  \cot52 \cot60°\cot78° \]

\[ = \tan\left( 90° - 12°  \right) \times \tan\left( 90° - 38\° \right) \times \cot52° \times \frac{1}{\sqrt{3}} \times \cot78° \] 

\[ = \frac{1}{\sqrt{3}} \times \tan78° \times \tan52° \times \cot52° \times \cot78° \]

\[ = \frac{1}{\sqrt{3}} \times \tan78° \times \tan52° \times \frac{1}{\tan52t° } \times \frac{1}{\tan78° }\]

\[ = \frac{1}{\sqrt{3}}\]

= RHS