Question

tan ${10}^o$ tan ${15}^o$ tan ${75}^o$ tan ${80}^o$ = ?

(a) $\sqrt{3}$ (b) $\frac{1}{\sqrt{3}}$ (c) -1 (d) 1

Answer 1

$tan{10}^{o}tan{15}^{o}tan{75}^{o}tan{80}^o=tan({90}^o-{80}^o)tan({90}^o-{75}^o)tan{75}^{o}tan{80}^o=cot{80}^{o}cot{75}^{o}tan{75}^{o}tan{80}^o=1$