Question

$\mathrm{If}\tan A=\frac{5}{12},\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\left(\sin A+\cos A\right)\sec A.\left[\mathrm{CBSE}2008\right]$

Answer 1

$$\begin{gathered} \left(\sin A+\cos A\right)\sec A \\ =\left(\sin A+\cos A\right)\frac{1}{\cos A} \\ =\frac{\sin A}{\cos A}+\frac{\cos A}{\cos A} \\ =\tan A+1 \\ =\frac{5}{12}+\frac{1}{1} \\ =\frac{5+12}{12} \\ =\frac{17}{12} \end{gathered}$$