Question

Prove that :

$\tan {10}^o\tan {15}^o\tan {75}^o\tan {80}^o=1$

Answer 1

L.H.S.

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

$=\tan ({90}^o-{80}^o)\tan ({90}^o-{75}^o)\tan {75}^o\tan {80}^o$

$=\cot {80}^o\cot {75}^o\tan {75}^o\tan {80}^0$

$=1$