Answer:
[tex] x = \frac{\pi}{3} + 2n\pi \\ or\\ x=\frac{-\pi}{3} + 2n\pi [/tex]
where "n" is an integer that belongs to Z.
Explanation:
The equation given is:
2cos²(x) - 5cos(x) + 2 = 0
To factor this equation, we will use the quadratic formula shown in the attached image.
From the given equation:
a = 2
b = -5
c = 2
This means that:
either cos(x) = [tex] \frac{5+\sqrt{(-5)^2-4(2)(2)}}{2(2)} = 2 [/tex] .......> This solution is rejected as the value of the cosine function lies between -1 and 1 only.
or cos(x) = [tex] \frac{5-\sqrt{(-5)^2-4(2)(2)}}{2(2)} = 0.5 [/tex] ......> This solution is accepted as it lies within -1 and 1
Now, using the inverse of the cosine, we can find that:
[tex] x = \frac{\pi}{3} + 2n\pi \\ or\\ x=\frac{-\pi}{3} + 2n\pi [/tex]
where "n" is an integer that belongs to Z.
Hope this helps :)
