Of sin A=5/13 the evaluate 5 sin A- 2 cos A divided by tan A

Dear Student,

The question doesn't clearly state what is being divided by tan A, still, I’ll try to solve it by dividing only  2cos A by tan A & the whole expression by tan A

Now

if only 2 cos A is being divided by tan A then it is 

now by Pythagorean triplets, we know  

so cos A = 

so  

Hence 

Now if the whole expression is divided by tan A, then

the expression becomes 

= 

Hope it helps!