Final Answer
Step-by-step Solution
Problem to solve:
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Apply the trigonometric identity: $\displaystyle\cot(x)=\frac{\cos(x)}{\sin(x)}$
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 both sides of the equality are equal, we have proven the identity