Solve: $4 {cos}^{2} x + 6 {sin}^{2} x = 5$

x = n π + \frac{π}{2}

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x = n π - \frac{π}{3}

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x = n π \pm \frac{π}{4}

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None of these

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Solution

The correct option is C $x = n π \pm \frac{π}{4}$
Given, $4 {cos}^{2} x + 6 {sin}^{2} x = 5$

$\Rightarrow 4 {cos}^{2} x + 4 {sin}^{2} x + 2 {sin}^{2} x = 5$

$\Rightarrow 2 {sin}^{2} x = 1$

$\Rightarrow {sin}^{2} x = \frac{1}{2} = {(\frac{1}{\sqrt{2}})}^{2}$
$\Rightarrow x = n π \pm \frac{π}{4}$

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Solve: 4cos2x+6sin2x=5

The correct option is C x=nπ±π4Given, 4cos2x+6sin2x=5⇒4cos2x+4sin2x+2sin2x=5⇒2sin2x=1⇒sin2x=12=(1√2)2⇒x=nπ±π4

Solve: $4 {cos}^{2} x + 6 {sin}^{2} x = 5$