Answer:
Step-by-step explanation:
We have
[tex]\sin A=\frac{5}{13}[/tex]
Draw a right triangle where the side in front of the angle A is 5 and the hypothenuse is 13. Hence the length of the other angle is [tex]\sqrt{13^2-5^2}=12[/tex].
It follows that
[tex]\cos A=\frac{12}{13}[/tex] and [tex]\tan A= \frac{5}{12}.[/tex]
Subtitute this we obtain
[tex]5\sin A-\frac{2\cos A}{\tan A}=5\cdot \frac{5}{13}-\frac{12/13}{5/12}[/tex]
which is equal to
[tex]\frac{25}{13}-\frac{144}{65}=\frac{125-144}{165}=-\frac{19}{165}.[/tex]
