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  Solve $\sin 2 x+\cos 2 x=0$
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  $\sin 2 x+\cos 2 x=0$
  $\sin 2 x=-\cos 2 x$
  $\frac{\sin 2 x}{\cos 2 x}=-1$
  $\tan 2 x=-1 \longrightarrow 1$
  $\pi<x<2 \pi$
  $2 \pi<2 x<4 \pi$
  $\tan x$ is negative in second and fourth quadrant
  $\therefore \tan \frac{3 \pi}{4}=\tan \frac{7 \pi}{4}=\ldots \ldots=\tan (4 n-1) \frac{\pi}{4}=-1$
  $n=1,2,3, \ldots$
  But $2 \pi<2 x<4 \pi$
  $\therefore 2 x=\frac{11 \pi}{4}$ or $2 x=\frac{15 \pi}{4}$
  $x=\frac{11 \pi}{8}$ or $\frac{15 \pi}{8}$
  by Diamond (38,951 points)
  
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explanation: The document contains a math question and its corresponding solution. The question is to solve the equation $\sin 2x + \cos 2x = 0$, and the solution is provided step-by-step, leading to the final answers $x = \frac{11\pi}{8}$ or $x = \frac{15\pi}{8}$.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 0 like 0 dislike
  14 views
  Solve $\sin 2 x+\cos 2 x=0$
  solved
  | 14 views
  
  0 like 0 dislike
  $\sin 2 x+\cos 2 x=0$
  $\sin 2 x=-\cos 2 x$
  $\frac{\sin 2 x}{\cos 2 x}=-1$
  $\tan 2 x=-1 \longrightarrow 1$
  $\pi<x<2 \pi$
  $2 \pi<2 x<4 \pi$
  $\tan x$ is negative in second and fourth quadrant
  $\therefore \tan \frac{3 \pi}{4}=\tan \frac{7 \pi}{4}=\ldots \ldots=\tan (4 n-1) \frac{\pi}{4}=-1$
  $n=1,2,3, \ldots$
  But $2 \pi<2 x<4 \pi$
  $\therefore 2 x=\frac{11 \pi}{4}$ or $2 x=\frac{15 \pi}{4}$
  $x=\frac{11 \pi}{8}$ or $\frac{15 \pi}{8}$
  by Diamond (38,951 points)
  
  0 like 0 dislike
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding solution. The question is to solve the equation $\sin 2x + \cos 2x = 0$, and the solution is provided step-by-step, leading to the final answers $x = \frac{11\pi}{8}$ or $x = \frac{15\pi}{8}$.
  
  Label: question-and-answer