Final Answer
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n,\:x=0\:,\:\:n\in\Z$
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Step-by-step Solution
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1
Use the trigonometric identity: $1-\cos\left(2x\right)=2\sin\left(x\right)^2$
$2\sin\left(2x\right)^2=8\cos\left(x\right)\sin\left(2x^2\right)$
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$2\sin\left(2x\right)^2=8\cos\left(x\right)\sin\left(2x^2\right)$
Learn how to solve problems step by step online. Solve the trigonometric equation 1-cos(4x)=8cos(x)sin(2x^2). Use the trigonometric identity: 1-\cos\left(2x\right)=2\sin\left(x\right)^2. Grouping all terms to the left side of the equation. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). The power of a product is equal to the product of it's factors raised to the same power.
Final Answer
$x=\frac{1}{2}\pi+2\pi n,\:x=\frac{3}{2}\pi+2\pi n,\:x=0\:,\:\:n\in\Z$