Question

$\frac{si{n}^{2}3A}{si{n}^{2}A}-\frac{co{s}^{2}3A}{co{s}^{2}A}=$

Answer 1

$\frac{{\sin }^{2}3A}{{\sin }^{2}A}-\frac{{\cos }^{2}3A}{{\cos }^{2}A}=\frac{{\sin }^{2}3A{\cos }^{2}3A-{\cos }^{2}3A{\sin }^{2}A}{{\sin }^{2}A{\cos }^{2}A}$

we know that $\sin (a-b)=\sin a\cos b-\cos a\sin b$

$\frac{{\sin }^2(3A-A)}{{\sin }^{2}A{\cos }^{2}A}\Rightarrow \frac{{\sin }^{2}A}{{\sin }^{2}A{\cos }^{2}A}[\because \sin 2\theta =2\sin \theta \cos \theta ]$

$\Rightarrow \frac{4{\sin }^{2}A{\cos }^{2}A}{{\sin }^{2}A{\cos }^{2}A}=4$