Final answer to the problem
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$
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Step-by-step Solution
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- Express in terms of sine and cosine
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1
Simplify $\cos\left(x\right)\csc\left(x\right)$ into $\cot(x)$ by applying trigonometric identities
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$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)+\cot\left(x\right)$
Learn how to solve problems step by step online. Solve the trigonometric equation tan(x)+cos(x)csc(x)=sec(x)csc(x)+cot(x). Simplify \cos\left(x\right)\csc\left(x\right) into \cot(x) by applying trigonometric identities. Move everything to the left hand side of the equation. Cancel like terms \cot\left(x\right) and -\cot\left(x\right). Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.
Final answer to the problem
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n\:,\:\:n\in\Z$
