If tan A = ⅔ , then what is the value of the following
(5 sin² A-2 cos² A)÷(15 sin² A+3 cos²A)

Given: ​

​$$\tan A = \frac{2}{3}$$ 

for a right angle triangle; 

​$$\tan A = \frac{ \text{Perpendicular}}{\text{Base}}$$ 

​$$\sin A = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$$ 

$$\cos A = \frac{\text{Base}}{\text{Hypotenuse}}$$ 

Pythagorus theorem: 

​$$(Hypotenuse)^2 = (Perpendicular)^2 + ( Base)^2$$ 

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