Question

$tan(si{n}^{-1}\frac{3}{5}+co{t}^{-1}\frac{3}{2})$

Answer 1

$tan(si{n}^{-1}\frac{3}{5}+co{t}^{-1}\frac{3}{2})\Rightarrow tan[ta{n}^{-1}\frac{\frac{3}{5}}{{\sqrt{1-\left(\frac{3}{5}\right)}}^2}+ta{n}^{-1}\frac{2}{3}][\because si{n}^{-1}x=ta{n}^{-1}\frac{x}{\sqrt{1-x^2}}andco{t}^{-1}\frac{x}{y}=ta{n}^{-1}\frac{y}{x}]=tan[ta{n}^{-1}\frac{3}{4}+ta{n}^{-1}\frac{2}{3}]=tan\left[ta{n}^{-1}\frac{(\frac{3}{4}+\frac{2}{3})}{1-\frac{3}{4}\times \frac{2}{3}}\right]=tan\left[ta{n}^{-1}\frac{\frac{17}{12}}{\frac{1}{2}}\right][\because ta{n}^{-1}x+ta{n}^{-1}y=ta{n}^{-1}\left(\frac{x+y}{1-xy}\right)]=tan\left[ta{n}^{-1}\frac{17}{6}\right]=\frac{17}{6}$