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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Trigonometry

JEE Advanced · Mathematics · Trigonometry

If |x^2-(π)/(4)+ x-2|=|x^2-2|+| x|+(π)/(4) then

If \left|x^2-\frac{\pi}{4}+\sin x-2\right|=\left|x^2-2\right|+|\sin x|+\frac{\pi}{4}thenthen

Options

  1. Ax∈(0,2)x \in(0, \sqrt{2})
  2. Bx∈(−2,2)x \in(-\sqrt{2}, \sqrt{2})
  3. Cx∈Rx \in R
  4. Dx∈(−2,0)x \in(-\sqrt{2}, 0)

Correct answer

D. x∈(−2,0)x \in(-\sqrt{2}, 0)

Step-by-step solution

∣x+y+z∣=∣x∣+∣y∣+∣z∣⇒x2−2<0,sin⁡x<0x∈(−2,0)\begin{aligned} & |x+y+z|=|x|+|y|+|z| \\ & \Rightarrow x^2-2 \lt 0, \sin x \lt 0 \\ & x \in(-\sqrt{2}, 0)\end{aligned}
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