Q32 / 90 · JEE Main 2011 · Mathematics

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

  • A
    $\frac{13}{16} \leq \mathrm{A} \leq 1$
  • B
    $1 \leq \mathrm{A} \leq 2$
  • C
    $\frac{3}{4} \leq \mathrm{A} \leq \frac{13}{16}$
  • Correct answer
    D
    $\frac{3}{4} \leq \mathrm{A} \leq 1$

Solution

$A=\sin ^2 x+\cos ^4 x=\frac{7+\cos 4 x}{8} \Rightarrow \frac{3}{4} \leq A \leq 1$

Hence, the correct answer is option: 'D'.

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