Question

The value of $tan(co{s}^{-1}\frac{4}{5}+ta{n}^{-1}\frac{2}{3})$ is

• A. $\frac{6}{17}$
• B. $\frac{17}{6}$
• C. $\frac{16}{7}$
• D. none of these

Answer 1

Answer: (B)

$tan(co{s}^{-1}\frac{4}{5}+ta{n}^{-1}\frac{2}{3})$
$=tan(ta{n}^{-1}(\frac{3}{4})+ta{n}^{-1}\frac{2}{3})$
$=\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}.\frac{2}{3}}=\frac{17}{6}$