# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\cos\left(x\right)\cdot\cot\left(x\right)=\frac{1}{\sin\left(x\right)}-\sin\left(x\right)$

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

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

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)cot(x)=1/(sin(x)-sin(x). Combine \frac{1}{\sin\left(x\right)}-\sin\left(x\right) in a single fraction. When multiplying two powers that have the same base (\sin\left(x\right)), you can add the exponents. Apply the identity: 1-\sin\left(x\right)^2=\cos\left(x\right)^2. Rewrite \frac{\cos\left(x\right)^2}{\sin\left(x\right)} as \cot\left(x\right)\cos\left(x\right) by applying trigonometric identities.

true
$\cos\left(x\right)\cdot\cot\left(x\right)=\frac{1}{\sin\left(x\right)}-\sin\left(x\right)$

### Main topic:

Trigonometric Identities

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### Time to solve it:

~ 0.04 s (SnapXam)