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# Prove the trigonometric identity $\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

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## Step-by-step Solution

Problem to solve:

$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

Specify the solving method

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Applying the trigonometric identity: $\cot\left(\theta\right)=\frac{1}{\tan\left(\theta\right)}$

$\tan\left(x\right)+\frac{1}{\tan\left(x\right)}=\sec\left(x\right)\csc\left(x\right)$

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

$\tan\left(x\right)+\frac{1}{\tan\left(x\right)}=\sec\left(x\right)\csc\left(x\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)+cot(x)=sec(x)csc(x). Applying the trigonometric identity: \cot\left(\theta\right)=\frac{1}{\tan\left(\theta\right)}. Combine all terms into a single fraction with \tan\left(x\right) as common denominator. When multiplying two powers that have the same base (\tan\left(x\right)), you can add the exponents. Applying the trigonometric identity: \tan(x)^2+1=\sec(x)^2.

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### Explore different ways to solve this problem

Prove from LHS (left-hand side)Prove from RHS (right-hand side)Express everything into Sine and Cosine
$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

### Main topic:

Trigonometric Identities

~ 0.13 s