Fractions In Fractions? Too Much!

Geometry Level 2

We know that the identity \( \dfrac{\sin x}{\cos x} = \tan x\) is true. Would the equation still holds true if we replace all the trigonometric functions with their reciprocal counterparts? That is, is the following identity true as well?

\[ \dfrac{ \csc x}{\sec x} = \cot x \]

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