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# Prove the trigonometric identity $\frac{\csc\left(x\right)}{\cot\left(x\right)}=\sec\left(x\right)$

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## Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

$\frac{\frac{1}{\sin\left(x\right)}}{\cot\left(x\right)}=\sec\left(x\right)$

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

$\frac{\frac{1}{\sin\left(x\right)}}{\cot\left(x\right)}=\sec\left(x\right)$

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

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

### Main topic:

Trigonometric Identities

~ 0.03 s