1. The problem is to simplify the expression $\sin^3 x \cdot \csc^2 x + \tan x \cdot \cos x$. 2. Recall the identities: - $\csc x = \frac{1}{\sin x}$, so $\csc^2 x = \frac{1}{\sin^2 x}$. - $\tan x = \frac{\sin x}{\cos x}$. 3. Substitute these into the expression: $$\sin^3 x \cdot \csc^2 x + \tan x \cdot \cos x = \sin^3 x \cdot \frac{1}{\sin^2 x} + \frac{\sin x}{\cos x} \cdot \cos x$$ 4. Simplify each term: - $\sin^3 x \cdot \frac{1}{\sin^2 x} = \sin^{3-2} x = \sin x$ - $\frac{\sin x}{\cos x} \cdot \cos x = \sin x$ 5. Add the simplified terms: $$\sin x + \sin x = 2 \sin x$$ 6. Therefore, the simplified expression is: $$2 \sin x$$