Find all solutions of the equation 2cosx-1=0 The answer is A+Bkpi and C+Dkpi where k is any integer, 0lt Alt Clt 2pi A= square Preview B= Preview C= square Preview D= Preview

To find all solutions of the equation $2\cos x - 1 = 0$, we can start by solving for $\cos x$.<br /><br />Step 1: Add 1 to both sides of the equation:<br />$2\cos x = 1$<br /><br />Step 2: Divide both sides by 2:<br />$\cos x = \frac{1}{2}$<br /><br />Now, we need to find the values of $x$ that satisfy this equation. The cosine function has a period of $2\pi$, which means that the solutions will repeat every $2\pi$ radians.<br /><br />Step 3: Find the angles whose cosine is $\frac{1}{2}$:<br />The angles whose cosine is $\frac{1}{2}$ are $\frac{\pi}{3}$ and $\frac{5\pi}{3}$.<br /><br />Step 4: Write the general solution:<br />The general solution for the equation $2\cos x - 1 = 0$ is $x = \frac{\pi}{3} + Bk\pi$ and $x = \frac{5\pi}{3} + Dk\pi$, where $k$ is any integer.<br /><br />Therefore, the values of $A$, $B$, $C$, and $D$ are:<br />$A = \frac{\pi}{3}$<br />$B = \pi$<br />$C = \frac{5\pi}{3}$<br />$D = \pi$<br /><br />So, the final answer is:<br />$A = \frac{\pi}{3}$<br />$B = \pi$<br />$C = \frac{5\pi}{3}$<br />$D = \pi$