The equation sqrt{3} sin x + cos x = 4 has | vedclass

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(D) The given equation is $\sqrt{3} \sin x + \cos x = 4$. This is of the form $a \sin x + b \cos x = c$,where $a = \sqrt{3}$,$b = 1$,and $c = 4$. The

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(D) The given equation is $\sqrt{3} \sin x + \cos x = 4$. This is of the form $a \sin x + b \cos x = c$,where $a = \sqrt{3}$,$b = 1$,and $c = 4$. The maximum value of the expression $a \sin x + b \cos x$ is $\sqrt{a^2 + b^2}$. Here,$\sqrt{a^2 + b^2} = \sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{3 + 1} = \sqrt{4} = 2$. Since the maximum value of $\sqrt{3} \sin x + \cos x$ is $2$ and the given equation requires the value to be $4$,which is greater than $2$,the equation has no solution.

The equation $\sqrt{3} \sin x + \cos x = 4$ has

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