The variable x satisfying the equation |sin x | vedclass

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(D) The given equation is $|\sin x \cos x| + \sqrt{2 + 	an^2 x + \cot^2 x} = \sqrt{3}$.We know that $2 + 	an^2 x + \cot^2 x = 1 + 	an^2 x + 1 + \co

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non-existent

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(D) The given equation is $|\sin x \cos x| + \sqrt{2 + 	an^2 x + \cot^2 x} = \sqrt{3}$.We know that $2 + 	an^2 x + \cot^2 x = 1 + 	an^2 x + 1 + \cot^2 x = \sec^2 x + \csc^2 x = \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} = \frac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x} = \frac{1}{\sin^2 x \cos^2 x}$.Thus,$\sqrt{2 + 	an^2 x + \cot^2 x} = \sqrt{\frac{1}{\sin^2 x \cos^2 x}} = \frac{1}{|\sin x \cos x|}$.Let $y = |\sin x \cos x|$. Since $0 The equation becomes $y + \frac{1}{y} = \sqrt{3}$.However,for any $y > 0$,by the $AM$-$GM$ inequality,$y + \frac{1}{y} \geq 2$.Since $\sqrt{3} \approx 1.732 Therefore,the solution is non-existent.

The variable $x$ satisfying the equation $|\sin x \cos x| + \sqrt{2 + \tan^2 x + \cot^2 x} = \sqrt{3}$ belongs to the interval

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