Question

Find the general solution of:
 $ 2\cos x = 1 $

Answer 1

Hint: In order to solve this question we will have to find the general solution and so for this we will find the value of x in in the first quadrant where it is equal to $ \dfrac{1}{2} $ and then we will find the value of x then as we know that the values will be repeated when we will move in the quadrant for every single time that will be added every time.

Complete step by step solution:
For solving this question we will first learn what are the general solutions:
So the general solution is the value of solutions in between 0 to $ 2\pi $ .
So we will find the first value of $ \cos x = \dfrac{1}{2} $ will be at $ \dfrac{\pi }{3} $
Now we will find the general value as the value will be repeated every time when we will move to the quadrant.
So the general solution will be \[x = 2k\pi \pm \dfrac{\pi }{3}\] where k is an integer.
By finding the general solution to every value of this equation.
So, the correct answer is “\[x = 2k\pi \pm \dfrac{\pi }{3}\]”.

Note: While solving these types of questions we should always keep in mind that there will be always two angles for the principle solutions of these questions. One angle will be directly found through the first quadrant and its complementary angle. So like this we will solve these questions. And that value will be repeated every single time on moving the quadrant.