Question

If $\tan x+\tan y=\frac{5}{6}$ and $\cot x+\cot y=5$, then $\tan (x+y)$ is

• A. $\frac{6}{5}$
• B. $\frac{5}{6}$
• C. $5$
• D. $6$
• E. $1$

Answer 1

Answer: (E)

$\tan x+\tan y=\frac{5}{6},\cot x+\cot 9=5$
$\frac{1}{\tan x}+\frac{1}{\tan y}=5$
$\frac{\tan x+\tan y}{\tan x\tan y}=5$
$\frac{5}{6\times 5}=\tan x\tan y$
$\tan t\tan y=\frac{1}{6}$
$\tan (x+y)=\frac{\tan x+\tan y}{1-\tan x\cdot \tan y}$
$=\frac{\frac{5}{6}}{1-\frac{1}{6}}=1$