Question

$\tan {20}^{\circ }+2\tan {50}^{\circ }=$

• A. $\tan {20}^{\circ }$
• B. $\cot {20}^{\circ }$
• C. $\tan {50}^{\circ }$
• D. $\cot {50}^{\circ }$

Answer 1

The correct option is B $\cot {20}^{\circ }$

$\tan 20°+2\tan 50°$

$=\tan 20°+\tan 50°+\tan 50°$

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$

$\Rightarrow \tan A+\tan B=\tan (A+B)\times (1-\tan A\tan B)$

$\tan 20°+\tan 50°+\tan 50°$

$=\tan (50°+20°)(1-\tan 20°\tan 50°)+\tan 50°$

$=\tan 70°(1-\tan 20°\cot 20°)+\tan 50°$

$=\tan 70°(1-1)+\tan 50°$

$=\tan 50°=\cot 20°$