Question

If $\cos A=\frac{5}{13}$ and A is not in first quadrant, then find the value of $\frac{\sin A-\cos A}{\tan A+1}$

Answer 1

Given,

$\cos A=\frac{5}{13}$ and A is not in first quadrant.

A is in 4th quadrant.

$\sin A=\frac{-12}{13}$ and $\tan A=\frac{-12}{5}$

Now,

$\frac{\sin A-\cos A}{\tan A+1}=\frac{-\frac{12}{13}-\frac{5}{13}}{-\frac{12}{5}+1}=-\frac{17}{13}\times -\frac{5}{7}=\frac{85}{91}$