Answer:Step-by-step explanation:[tex]\frac{sin3A}{cosA} + \frac{cos3A}{sinA}[/tex][tex]\frac{sin3AsinA}{sinAcosA} + \frac{cos3AcosA}{sinAcosA}[/tex][tex]\frac{cos3AcosA + sin3AsinA}{sinAcosA}[/tex]From here, remember the following identity:[tex]cos(X - Y) = cosXcosY + sinXsinY[/tex]If we set [tex]X = 3A[/tex] and [tex]Y = A[/tex], we get the following:[tex]cos(3A - A) = cos2A = cos3AcosA + sin3AsinA[/tex]we can then plug this back into our original equation:[tex]\frac{cos2A}{sinAcosA}[/tex]From here, remember the following identity:[tex]cos2A = cos^{2}A - sin^{2}A[/tex]we can then plug this back into our original equation:[tex]\frac{cos^{2}A - sin^{2}A}{sinAcosA}[/tex][tex]\frac{cos^{2}A}{sinAcosA} - \frac{sin^{2}A}{sinAcosA}[/tex][tex]\frac{cosA}{sinA} - \frac{sinA}{cosA}[/tex][tex]cotA - tanA[/tex]