Final answer to the problem
$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$
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Step-by-step Solution
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- Express in terms of sine and cosine
- Simplify
- Simplify into a single function
- Express in terms of Sine
- Express in terms of Cosine
- Express in terms of Tangent
- Express in terms of Cotangent
- Express in terms of Secant
- Express in terms of Cosecant
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1
The reciprocal sine function is cosecant: $\frac{1}{\csc(x)}=\sin(x)$
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$8\sin\left(x\right)=2+4\sin\left(x\right)$
Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation 8sin(x)=2+4/csc(x). The reciprocal sine function is cosecant: \frac{1}{\csc(x)}=\sin(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. Combining like terms 8\sin\left(x\right) and -4\sin\left(x\right). Divide both sides of the equation by 4.
Final answer to the problem
$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$
