There is more than one way to solve this. One way is to use trig identities.I will use the following method.
sinA = opposite / hypotenuse
cosA = adjacent / hypotenuse
tanA = opposite / adjacent
If 5tanA = 4 then tanA = 4/5.
This describes a triangle where the opposite is length 4 and the adjacent is length 5.
Let "a" be the opposite, "b" the adjacent and "c" is the hypotenuse.
a = 4
b = 5
From this, derive:
sinA = 4/c
cosA = 5/c
Use these values to rewrite the equation
[5sinA + 3cosA] / [sinA - 2cosA]
[5(4/c) + 3(5/c)] / [(4/c - 2(5/c)]
[20/c + 15/c] / [(4/c - 10/c)]
[35/c] / [-6/c]
Eliminate "c" by multiplying this equation by c/c which is the same as multiplying by 1.
-35/6
