Question

Find the value of $\tan {15}^o\tan {60}^o\tan {75}^o$.

Answer 1

$\tan {15}^{\circ }\tan {60}^{\circ }\tan {75}^{\circ }$

$=\tan {15}^{\circ }\tan {60}^{\circ }\tan (90-15)$

$=\tan {15}^{\circ }\tan {60}^{\circ }\cot {15}^{\circ }$ since $\tan (90-\theta )=\cot \theta$

$=1\times \sqrt{3}$ since $\tan \theta \cot \theta =1$ and $\tan {60}^{\circ }=\sqrt{3}$

$=\sqrt{3}$