# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\csc\left(2x\right)-2=0$

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

$\csc\left(2x\right)=2$

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation csc(2*x)-2=0. We need to isolate the dependent variable x, we can do that by subtracting -2 from both sides of the equation. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Take the reciprocal of both sides of the equation. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right).

$x=0+2\pi n,\:x=\pi+2\pi n,\:x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n$
$\csc\left(2x\right)-2=0$