If A = sin 2 x + cos 4 x , then for all real x, 16 13 ≤ A ≤ 1, 1 ≤ A ≤ 2, 4 3 ≤ A ≤ 16 13 , 4 3 ≤ A ≤ 1

A = sin 2 x + cos 4 x = 8 7 + c o s 4 x ⇒ 4 3 ≤ A ≤ 1

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

Question: Answered & Verified by Expert

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

MathematicsTrigonometric EquationsJEE MainJEE Main 2011

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1675 Upvotes Verified Answer

The correct answer is:
$\frac{3}{4} \leq \mathrm{A} \leq 1$

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

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