Simplify the expression $\cos \left(\theta \right)\csc \left(\theta \right)\sin \left(\theta \right)\cot \left(\theta \right)$.

• A. $\frac{{\cos }^2}{\left(}$
• B. $\frac{{\cos }^2}{\left(}$
• C. $\frac{{\cos }^2}{\left(}$
• D. ${\cos }^2\left(\theta \right)\frac{1}{\sin }\left(\theta \right)$

Answer: (B)

Verified step by step guidance

1. Start by writing the original expression clearly: \(\cos(\theta) \cdot \csc(\theta) \cdot \sin(\theta) \cdot \cot(\theta)\).
2. Recall the definitions of the trigonometric functions involved: \(\csc(\theta) = \frac{1}{\sin(\theta)}\) and \(\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}\).
3. Substitute these definitions into the expression to rewrite it entirely in terms of sine and cosine: \(\cos(\theta) \cdot \frac{1}{\sin(\theta)} \cdot \sin(\theta) \cdot \frac{\cos(\theta)}{\sin(\theta)}\).
4. Simplify the expression step-by-step by canceling common factors, such as \(\sin(\theta)\) in numerator and denominator, and combining like terms.
5. After simplification, express the final result as a fraction involving powers of cosine and sine, for example, \(\frac{\cos^{2}(\theta)}{\sin(\theta)}\).