Question

The value of $\tan {40}^o+2\tan {10}^o$ is equal to

• A. $\cot {50}^o$
• B. $\cot {40}^o$
• C. $\cot {10}^o$
• D. $\cot {30}^o$

Answer 1

Answer: (B)

$\cot {40}^o$

$\tan 40°+2\tan 10°=\tan 40°+2\cot 80°=\tan 40°+\frac{2}{\tan 80°}\tan 80°=\frac{2\tan 40°}{1-{\tan }^{2}40°}=\tan 40°+\frac{2(1-{\tan }^{2}40°)}{2\tan 40°}=\frac{{\tan }^{2}40°+1-{\tan }^{2}40°}{\tan 40°}=\cot 40°or\tan 50°$