Question

Prove that :

$\tan 5^o\tan {25}^o\tan {30}^o\tan {65}^o\tan {85}^o=\frac{1}{\sqrt{3}}$

Answer 1

LHS :

$\tan 5^o\tan {25}^o\tan {30}^o\tan {65}^o\tan {85}^o$

$=\left(\tan 5^o\tan {85}^o\right)\left(\tan {25}^o\tan {65}^o\right)\tan {30}^o$

$=\left(\tan 5^o\cot 5^o\right)\left(\tan {25}^o\cot {25}^o\right)\tan {30}^o$

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