How do you solve 4 cosine squared x - 2 equals 0?

Answer 1

Let c represent cos x.

Then, we have,

4c2 - 2 = 0; whence,

4c2 = 2,

c2 = ½, and

c = ±√½ = ±½√2; that is,

cos x = ±½√2.

From this, it is evident that,

for 0 ≤ x < 360°, x = 45°, 135°, 225°, or 315°;

or, if you prefer,

for 0 ≤ x < 2π, x = ¼π, ¾π, 1¼π, or 1¾ π.