Question

Given, $12\cot A=5$, the value of $\frac{\sin A+\cos A}{\sin A-\cos A}$ is $\frac{17}{p}$ then p=

Answer 1

$\cot A=\frac{5}{12}$

$\frac{\sin A+\cos A}{\sin A-\cos A}$

$\Rightarrow$ Divide numerator & denominator by $\sin A$

$\Rightarrow \frac{1+\cot A}{1-\cot A}$

$\Rightarrow \frac{1+\frac{5}{12}}{1-\frac{5}{12}}=\frac{12+5}{12-5}=\frac{17}{7}$.