Starting from the left-hand side (LHS) of the identity

Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

Multiplying fractions $\frac{\cos\left(x\right)}{\sin\left(x\right)} \times \frac{1}{\cos\left(x\right)}$

Simplify the fraction $\frac{\cos\left(x\right)}{\sin\left(x\right)\cos\left(x\right)}$ by $\cos\left(x\right)$

The reciprocal sine function is cosecant: $\frac{1}{\sin(x)}=\csc(x)$

Since we have reached the expression of our goal, we have proven the identity