Question

If $(2\cos x - 1)(3 + 2\cos x) = 0$, then $\cos x = \frac{1}{2}\text{ }$

• A. $\cos x \neq \frac{- 3}{2}$
• B. $\Rightarrow$ $x = 2n\pi \pm \frac{\pi}{3};\left\{ \begin{aligned} & n = 0ds\ fy,,x = \frac{\pi}{3},\frac{5\pi}{3} \\ & n = 1ds\ fy,,x = \frac{5\pi}{3} \end{aligned} \right\}$
• C. $81^{\sin^{2}x} + 81^{\cos^{2}x} = 30$
• D. $x = \frac{\pi}{6}$

Answer 1

Answer: (B)

$\Rightarrow$ $x = 2n\pi \pm \frac{\pi}{3};\left\{ \begin{aligned} & n = 0ds\ fy,,x = \frac{\pi}{3},\frac{5\pi}{3} \\ & n = 1ds\ fy,,x = \frac{5\pi}{3} \end{aligned} \right\}$

Answer 2

$\therefore\sin\theta + \cos\theta = \frac{1}{2}$

For $\sin\left( \theta + \frac{\pi}{4} \right) = \frac{1}{2\sqrt{2}}$

$R_{1} \rightarrow R_{1} - R_{3}$, we get $R_{2} \rightarrow R_{2} - R_{3}$.