Question

The value of $tan[si{n}^{-1}\left(\frac{3}{5}\right)+co{s}^{-1}\left(\frac{3}{\sqrt{13}}\right)]$ is

• A. $\frac{6}{17}$
• B. $\frac{6}{\sqrt{13}}$
• C. $\frac{\sqrt{13}}{5}$
• D. $\frac{17}{6}$

Answer 1

The correct option is D $\frac{17}{6}$

$tan[si{n}^{-1}\left(\frac{3}{5}\right)+co{s}^{-1}\left(\frac{3}{\sqrt{13}}\right)]$
$=tan(ta{n}^{-1}\frac{3}{4}+ta{n}^{-1}\frac{2}{3})=tan\left(ta{n}^{-1}\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}.\frac{2}{3}}\right)$
$=tan[ta{n}^{-1}\frac{17}{12}\times \frac{12}{6}]=\frac{17}{6}$.