simplify $$\frac{sin3A}{sinA}-\frac{cos3A}{cosA}$$?

$$\frac{sin3A}{sinA}-\frac{cos3A}{cosA}$$

$$\frac {( sin3A ) ( cosA ) -( cos3A ) ( sinA )}{sinAcosA}$$

$$\frac {[( 3sinA - 4sin³A ) cosA] - [( 4cos³A - 3cosA ) ( sinA )]} { sinAcosA}$$

$$\frac {3sinAcosA - 4sin³AcosA - 4cos³AsinA + 3sinAcosA} { sinAcosA}$$

$$\frac {6sinAcosA - 4sin³AcosA - 4cos³AsinA }{ sinAcosA}$$

$$= \frac{sinAcosA ( 6 - 4sin²A - 4cos²A )}{sinAcosA}$$

= 6 - 4sin²A - 4cos²A

= 6 - 4 ( sin²A + cos²A ) [ °.° $$ sin²\theta + cos² \theta $$= 1]

= 6 - 4 × 1

= 6 - 4

= 2