b) \( \cos x \sin ^{2} x+\cos ^{3} x=\cos x \)

To solve the equation \( \cos x \sin^2 x + \cos^3 x = \cos x \), first, we can factor out \( \cos x \): \[ \cos x (\sin^2 x + \cos^2 x) = \cos x \] Since \( \sin^2 x + \cos^2 x = 1 \), we can substitute this into the equation: \[ \cos x (1) = \cos x \] This simplifies to: \[ \cos x = \cos x \] This equation is trivially true for any \( x \) where \( \cos x \) is defined and is not zero. Therefore, we must consider the implications of \( \cos x = 0 \), which gives specific solutions. The cosine function is zero at odd multiples of \( \frac{\pi}{2} \): \[ x = \frac{\pi}{2} + n\pi, \quad n \in \mathbb{Z} \] Thus, the complete solution set includes all \( x \) for which \( \cos x \) does not lead to division by zero and all odd multiples of \( \frac{\pi}{2} \).