# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\csc\left(x\right)+\sin\left(x\right)=\cot\left(x\right)\cdot\cos\left(x\right)$

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

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

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation csc(x)+sin(x)=cot(x)cos(x). Apply the trigonometric identity: \cot\left(x\right)=\frac{\cos\left(x\right)}{\sin\left(x\right)}. Multiplying the fraction by \cos\left(x\right). When multiplying two powers that have the same base (\cos\left(x\right)), you can add the exponents. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.

$x=0+2\pi n,\:x=2\pi+2\pi n,\:x=\pi+2\pi n$
$\csc\left(x\right)+\sin\left(x\right)=\cot\left(x\right)\cdot\cos\left(x\right)$