Cos 2x = 2 cos x where x is between 0 to 360 degree in trigonometrics?
2 Answers
The solutions are
Explanation:
We need
Therefore,
This is a quadratic equation in
The discriminant is
As
Explanation:
By the double angle formula
So
implies
or
Using the quadratic formula, this gives solutions at
but
we know
so only
Using the
(from here on I will approximate this as
This is equivalent to a reference angle of
and
we know that (based on CAST) there will be another angle in the range