iran-konkur 2023 Q13

iran-konkur · Other · konkur-riazi_1402_general Trigonometric equations in context
13. In the trigonometric equation $m(\cos x - \sin x) - 3\sqrt{6}\sin(2x) = \sqrt{6}$, if $\cos(x + \dfrac{\pi}{4}) = \dfrac{1}{\sqrt{3}}$, what is the value of $m$?
\[ \text{(1) } -6 \qquad \text{(2) } -3 \qquad \text{(3) } 6 \qquad \text{(4) } 3 \]
\textbf{13.} In the trigonometric equation $m(\cos x - \sin x) - 3\sqrt{6}\sin(2x) = \sqrt{6}$, if $\cos(x + \dfrac{\pi}{4}) = \dfrac{1}{\sqrt{3}}$, what is the value of $m$?

\[
\text{(1) } -6 \qquad \text{(2) } -3 \qquad \text{(3) } 6 \qquad \text{(4) } 3
\]