Question

If $8\tan A=15$, then the value of $\frac{\sin A-\cos A}{\sin A+\cos A}$ is:

• A. $\frac{7}{23}$
• B. $\frac{11}{23}$
• C. $\frac{13}{23}$
• D. $\frac{17}{23}$

Answer 1

The correct option is A $\frac{7}{23}$

$8\tan A=15\Rightarrow \tan A=\frac{15}{8}$
Now, $\frac{\sin A-\cos A}{\sin A+\cos A}$
Multiply and divide by $\cos A$
$=\frac{\frac{\sin A}{\cos A}-\frac{\cos A}{\cos A}}{\frac{\sin A}{\cos A}+\frac{\cos A}{\cos A}}$

$=\frac{\tan A-1}{\tan A+1}$

Now, substitute the value of $\tan A$
$=\frac{\frac{15}{8}-1}{\frac{15}{8}+1}$

$=\frac{7}{23}$