384. $\frac{1-\cos ^{2} x}{1-\sin ^{2} x}+\operatorname{tg} x \operatorname{ctg} x$.

384. $\frac{1-\cos ^{2} x}{1-\sin ^{2} x}+\tan x \cot x$.
Solution. Applying the formulas $1-\cos ^{2} \alpha=\sin ^{2} \alpha, 1-\sin ^{2} \alpha=$ $=\cos ^{2} \alpha$ and identities IV and VI, we find

$$
\frac{1-\cos ^{2} x}{1-\sin ^{2} x}+\operatorname{tg} x \operatorname{ctg} x=\frac{\sin ^{2} x}{\cos ^{2} x}+1=\operatorname{tg}^{2} x+1=\frac{1}{\cos ^{2} x}
$$