[JEE Main 2011] if a sin 2x cos 4x then for all real x
If $A=\sin^2x+\cos^4x$, then for all real $x$
(a) $\frac{13}{16}\le A\le1$
(b) $1\le A\le2$
(c) $\frac34\le A\le\frac{13}{16}$
(d) $\frac34\le A\le1$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (d) $\frac34\le A\le1$
Let $s=\sin^2x$: $A=s+(1-s)^2=s^2-s+1$, minimum $\frac34$ at $s=\frac12$, maximum $1$ at $s=0,1$. So $\frac34\le A\le1$.
JEE Main 2011 · Trigonometry — verified solution by the Vidaara Team.
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