Answer:
I think it always work out because they try to manipulate the equation such that you'll get 3
you can actually use other values apart from the ones used
the set is a {1/3, 2/3, 1, 4/3, ...} infinite set and {1/3, 2/3, 1, 4/3, ...} all numbers are subsets of the real numbers.
In mathematics, a real number is a continuous quantity value that can represent a distance along a line. The adjective real number in this context was introduced by Rene Descartes in the 17th century. Rene Descartes distinguished between real and imaginary roots of polynomials.
Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions (1/2, 2.5), and irrational numbers such as √3 and π(22/7) are all real numbers.
Learn more about real numbers here
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This is the concept of algebra, to solve the expression we proceed as follows;
cos 2x-cosx=0
cos 2x=cosx
but:
cos 2x+1=2(cos^2x)
thereore;
from:
cos 2x=cos x
adding 1 on both sides we get:
cos 2x+1=cos x+1
2(cos^2x)=cosx+1
suppose;
cos x=a
thus;
2a^2=a+1
a^2-1/2a-1/2=0
solving the above quadratic we get:
a=-0.5 and a=1
when a=-0.5
cosx=-0.5
x=120=2/3π
when x=1
cos x=1
x=0
the answer is:
x=0 or x=2/3π
