Question

$\tan 6^o\tan {42}^o\tan {66}^o\tan {78}^o=$

Answer 1

We know that tanx×tan(60-x)×tan(60+x)=tan(3x)

$\frac{tan{6}^{0}tan{54}^{0}tan{66}^{0}tan{78}^{0}tan{42}^0}{tan54}=\frac{tan{18}^{0}tan{42}^{0}tan{78}^0}{tan{54}^0}=1$

(by applying above identity two times)