The value of x, which satisfies the equation | vedclass

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(D) We know that $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$,$\operatorname{cosec} 30^{\circ} = \frac{1}{\sin 30^{\circ}} = \frac{1}{1/2} = 2$,and $	an 30

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) We know that $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$,$\operatorname{cosec} 30^{\circ} = \frac{1}{\sin 30^{\circ}} = \frac{1}{1/2} = 2$,and $	an 30^{\circ} = \frac{1}{\sqrt{3}}$.Substituting these values into the given equation:$2(2)^{2} + x(\frac{\sqrt{3}}{2})^{2} - \frac{3}{4}(\frac{1}{\sqrt{3}})^{2} = 10$$2(4) + x(\frac{3}{4}) - \frac{3}{4}(\frac{1}{3}) = 10$$8 + \frac{3x}{4} - \frac{1}{4} = 10$Multiply the entire equation by $4$ to eliminate the denominators:$32 + 3x - 1 = 40$$31 + 3x = 40$$3x = 40 - 31$$3x = 9$$x = 3$

The value of $x,$ which satisfies the equation $2 \operatorname{cosec}^{2} 30^{\circ} + x \sin^{2} 60^{\circ} - \frac{3}{4} \tan^{2} 30^{\circ} = 10$ is

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