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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2011 · Mathematics · Trigonometric Equations

If A= ^2 x+ ^4 x , then for all real x

If A=sin⁡2x+cos⁡4xA=\sin ^2 x+\cos ^4 x, then for all real xx

Options

  1. A1316≤A≤1\frac{13}{16} \leq \mathrm{A} \leq 1
  2. B1≤A≤21 \leq \mathrm{A} \leq 2
  3. C34≤A≤1316\frac{3}{4} \leq \mathrm{A} \leq \frac{13}{16}
  4. D34≤A≤1\frac{3}{4} \leq \mathrm{A} \leq 1

Correct answer

D. 34≤A≤1\frac{3}{4} \leq \mathrm{A} \leq 1

Step-by-step solution

A=sin⁡2x+cos⁡4x=7+cos⁡4x8⇒34≤A≤1A=\sin ^2 x+\cos ^4 x=\frac{7+\cos 4 x}{8} \Rightarrow \frac{3}{4} \leq A \leq 1
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