Final answer to the problem
$x=\frac{1}{4}\pi+\pi n,\:x=\frac{5}{4}\pi+\pi n\:,\:\:n\in\Z$
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Step-by-step Solution
Learn how to solve factorization problems step by step online. Solve the trigonometric equation csc(x)=sin(x)tan(x)+cos(x). Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Multiplying the fraction by \sin\left(x\right).
Final answer to the problem
$x=\frac{1}{4}\pi+\pi n,\:x=\frac{5}{4}\pi+\pi n\:,\:\:n\in\Z$
