# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)$

Choose the solving method

Learn how to solve trigonometric identities problems step by step online.

$\frac{\cot\left(x\right)}{\cos\left(x\right)}=\csc\left(x\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cot(x)sec(x)=csc(x). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Apply the trigonometric identity: \cot\left(x\right)=\frac{\cos\left(x\right)}{\sin\left(x\right)}. Simplify the fraction \frac{\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).

## Final Answer

true
$\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)$

### Main topic:

Trigonometric Identities

### Time to solve it:

~ 0.03 s (SnapXam)