Question

Value of $\tan 15^{\circ }\cdot \tan 45^{\circ }\tan 75^{\circ }$ is

• A. $0$
• B. $1$
• C. $\frac{\sqrt{3}}{2}$
• D. $-1$

Answer 1

Answer: (B)

$\tan 15^{\circ }.\tan 45^{\circ }\tan 75^{\circ }=\tan 15^{\circ }.\tan \left(60^{\circ }-15^{\circ }\right).\tan \left(60^{\circ }+15^{\circ }\right)$
$=\tan \left(3\times 15^{\circ }\right)=\tan 45^{\circ }=1$