Answer:
To factorize the expression x^2 - 2x - cos(θ) = 0, we can use the quadratic formula. However, since the expression also involves the cosine function, it may not be possible to factorize it further.
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the following formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, the equation is x^2 - 2x - cos(θ) = 0, so we have:
a = 1
b = -2
c = -cos(θ)
Substituting these values into the quadratic formula, we get:
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-cos(θ)))) / (2(1))
Simplifying further:
x = (2 ± sqrt(4 + 4cos(θ))) / 2
x = (2 ± 2sqrt(1 + cos(θ))) / 2
x = 1 ± sqrt(1 + cos(θ))
Thus, the expression x^2 - 2x - cos(θ) = 0 cannot be factored further, and its solutions are given by x = 1 ± sqrt(1 + cos(θ)).