Limx - -sin4 x-sin2 x-1cos4 x-cos2 x-1is equal to

Lim_x → ∞sin^4 x sin^2 x+1cos^4 x cos^2 x+1 = nbsp;lim_x → ∞(1 cos^2 x)^2 (1 cos^2 x)+1cos^4 x cos^2 x+1 = lim_x → ∞cos^4 x cos^2 x+1cos^4 x cos^2 x+1 = 1 ...

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Byju's Answer

Standard XIII

Mathematics

Indeterminate Forms

limx → ∞sin4 ...

Question

$lim x \to \infty \frac{{sin}^{4} x - {sin}^{2} x + 1}{{cos}^{4} x - {cos}^{2} x + 1}$ is equal to

0

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1

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\frac{1}{3}

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Does not exist

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Solution

The correct option is B $1$
$lim x \to \infty \frac{{sin}^{4} x - {sin}^{2} x + 1}{{cos}^{4} x - {cos}^{2} x + 1}$
$= lim x \to \infty \frac{(1 - {cos}^{2} x)^{2} - (1 - {cos}^{2} x) + 1}{{cos}^{4} x - {cos}^{2} x + 1}$
$= lim x \to \infty \frac{{cos}^{4} x - {cos}^{2} x + 1}{{cos}^{4} x - {cos}^{2} x + 1}$
$= 1$

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limx → ∞sin4 x−sin2 x+1cos4 x−cos2 x+1is equal to

The correct option is B 1limx → ∞sin4 x−sin2 x+1cos4 x−cos2 x+1 =limx → ∞(1−cos2 x)2−(1−cos2 x)+1cos4 x−cos2 x+1 =limx → ∞cos4 x−cos2 x+1cos4 x−cos2 x+1 =1

$lim x \to \infty \frac{{sin}^{4} x - {sin}^{2} x + 1}{{cos}^{4} x - {cos}^{2} x + 1}$ is equal to