The solution of the equation $4 c o s^{2} x + 6 s i n^{2} x = 5$

x = n π \neq \frac{π}{2}

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x = n π \neq \frac{π}{4}

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x = n π \neq \frac{3 π}{2}

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None of these

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Solution

The correct option is D None of these
Consider given the trigonometry equation,

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

$4 (1 - {sin}^{2} x) + 6 {sin}^{2} x = 5$

$2 {sin}^{2} x + 4 = 5$

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

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

$sin x = \frac{1}{\sqrt{2}} o r sin x = - \frac{1}{\sqrt{2}}$

$sin x = sin \frac{π}{4} o r sin x = sin (- \frac{π}{4})$

$x = \frac{π}{4} o r x = - \frac{π}{4}$

$x = n π + {(- 1)}^{n} \frac{π}{4} o r x = n π - {(- 1)}^{n} \frac{π}{4}$

Hence, this is the answer.

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The solution of the equation 4cos2x+6sin2x=5

The correct option is D None of theseConsider given the trigonometry equation, 4cos2x+6sin2x=5 4(1−sin2x)+6sin2x=5 2sin2x+4=5 2sin2x=1 sin2x=12 sinx=1√2orsinx=−1√2 sinx=sinπ4orsinx=sin(−π4) x=π4orx=−π4 x=nπ+(−1)nπ4orx=nπ−(−1)nπ4 Hence, this is the answer.

The solution of the equation $4 c o s^{2} x + 6 s i n^{2} x = 5$