Question

tan $5^o$ tan ${25}^o$ tan ${30}^o$ tan ${65}^o$ tan ${85}^o$ = ?

(a) $\sqrt{3}$ (b) $\frac{1}{\sqrt{5}}$ (c) 1 (d) none of these

Answer 1

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

= cot $({90}^o-5^o)$ cot $(90-{25}^o)$ tan ${30}^o$ tan ${65}^o$ tan ${85}^o$

= cot ${85}^o$ cot ${65}^o$ tan ${30}^o$ tan ${65}^o$ tan ${85}^o$

= tan ${30}^o$ = $\frac{1}{\sqrt{3}}$

So, the correct choice is (d).