Question

The value of $\frac{\tan {60}^{\circ }-\tan {30}^{\circ }}{1+\tan {60}^{\circ }\tan {30}^{\circ }}$ equals

• A. $\tan {60}^{\circ }$
• B. $\tan 0^{\circ }$
• C. $\tan {30}^{\circ }$
• D. $\frac{1}{3}$

Answer 1

The correct option is C $\tan {30}^{\circ }$

$\frac{\tan {60}^0-\tan {30}^0}{1+\tan {60}^0.\tan {30}^0}$

$=\tan ({60}^0-{30}^0)$ $[\because \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A.\tan B}]$

$=\tan {30}^0$

$=\frac{1}{\sqrt{3}}$

Hence, the answer is $=\tan {30}^0.$