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# Prove the trigonometric identity $\tan\left(x\right)\cos\left(x\right)\csc\left(x\right)=1$

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## Step-by-step Solution

Problem to solve:

$\tan\left(x\right)\cdot \cos\left(x\right)\cdot \csc\left(x\right)=1$

Choose the solving method

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Apply the trigonometric identity: $\cos\left(x\right)\csc\left(x\right)$$=\cot\left(x\right)$

$\cot\left(x\right)\tan\left(x\right)=1$

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

$\cot\left(x\right)\tan\left(x\right)=1$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)cos(x)csc(x)=1. Apply the trigonometric identity: \cos\left(x\right)\csc\left(x\right)=\cot\left(x\right). The tangent function is inverse to the cotangent: \tan(x)=\frac{1}{\cot(x)}. Multiply the fraction and term. Simplify the fraction \frac{\cot\left(x\right)}{\cot\left(x\right)} by \cot\left(x\right).

true
$\tan\left(x\right)\cdot \cos\left(x\right)\cdot \csc\left(x\right)=1$

### Main topic:

Trigonometric Identities

~ 0.03 s