Answer
Please refer to the step-by-step [art below for the solution.
Work Step by Step
RECALL:
$\tan{\theta} = \dfrac{\sin{\theta}}{\cos{\theta}}
\\\csc{\theta} = \dfrac{1}{\sin{\theta}}$
Thus, the left side of the equation is equivalent to:
$\require{cancel}
\cos{\theta} \csc{\theta}\tan{\theta}$
$\\=\cos{\theta} \cdot \dfrac{1}{\sin{\theta}} \cdot \dfrac{\sin{\theta}}{\cos{\theta}}
\\=\cancel{\cos{\theta}} \cdot \dfrac{1}{\cancel{\sin{\theta}}} \cdot \dfrac{\cancel{\sin{\theta}}}{\cancel{\cos{\theta}}}
\\=1.$
Therefore,
$\cos{\theta} \csc{\theta}\tan{\theta}=1$