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Step-by-step Solution

Prove the trigonometric identity $\cot\left(2x\right)+\tan\left(x\right)=\csc\left(2x\right)$

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asin
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Answer

true

Step-by-step explanation

Problem to solve:

$cot\left(2x\right)+tan\left(x\right)=csc\left(2x\right)$
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Applying the cotangent identity: $\displaystyle\cot\left(\theta\right)=\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}$

$\frac{\cos\left(2x\right)}{\sin\left(2x\right)}+\tan\left(x\right)=\csc\left(2x\right)$
2

Using the sine double-angle identity

$\frac{\cos\left(2x\right)}{2\sin\left(x\right)\cos\left(x\right)}+\tan\left(x\right)=\csc\left(2x\right)$

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Answer

true
$cot\left(2x\right)+tan\left(x\right)=csc\left(2x\right)$

Main topic:

Trigonometric identities

Used formulas:

1. See formulas

Time to solve it:

~ 0.65 seconds