1. Simpritg the tollowing expresson 1. \( \tan x \cdot \cos x \) 12. \( \frac{(1+\cos x)(1-\cos x)}{\sin x} \) 1.3. \( \frac{1}{\cos \theta} \frac{1}{\cos ^{2} \theta}-1 \)

Let's simplify those trigonometric expressions! 1. For \( \tan x \cdot \cos x \), recall that \( \tan x = \frac{\sin x}{\cos x} \). So, substituting that in gives us: \[ \tan x \cdot \cos x = \frac{\sin x}{\cos x} \cdot \cos x = \sin x \] 2. The expression \( \frac{(1+\cos x)(1-\cos x)}{\sin x} \) simplifies using the difference of squares: \[ (1 + \cos x)(1 - \cos x) = 1 - \cos^2 x = \sin^2 x \] Therefore, we have: \[ \frac{\sin^2 x}{\sin x} = \sin x \] 3. For \( \frac{1}{\cos \theta} \frac{1}{\cos^2 \theta}-1 \), we can rewrite it as: \[ \frac{1}{\cos^3 \theta} - 1 = \sec^3 \theta - 1 \] So, the simplified forms of the three expressions are: 1. \( \sin x \) 2. \( \sin x \) 3. \( \sec^3 \theta - 1 \)