Answer
The statement is false.
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:
$\require{cancel}
\dfrac{\sin{\theta}}{\tan{\theta}}$
$\require{cancel}\\=\dfrac{\sin{\theta}}{\frac{\sin{\theta}}{\cos{\theta}}}
\\=\sin{\theta} \cdot \dfrac{\cos{\theta}}{\sin{\theta}}
\\=\cancel{\sin{\theta}} \cdot \dfrac{\cos{\theta}}{\cancel{\sin{\theta}}}
\\=\cos{\theta}$
With $\dfrac{\sin{\theta}}{\tan{\theta}}=\cos{\theta}$, the left side of the given equation is not equal to the right side.
The statement is false.
