# Step-by-step Solution

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## Step-by-step Solution

Problem to solve:

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

Choose the solving method

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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)}. Divide fractions \frac{\frac{1}{\sin\left(x\right)}}{\cot\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Simplify \sin\left(x\right)\cot\left(x\right) into \cos(x) by applying trigonometric identities. Applying the trigonometric identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.

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

### Main topic:

Trigonometric Identities

~ 0.04 s