Question

How do you solve `2(cosx+1)=1`?

Answer 1

The solution in the interval `(0, 2pi)` would be `(2pi)/3, (4pi)/3`

Explanation:

The given equation is `cos x +1= 1/2`

Or, `cos x=1/2-1= -1/2`. Cosine value is `1/2` for `x=pi/3`.

Cos x is negative in IInd and IIIrd Quarters. Hence `cos(pi-x)` and `cos (pi+x)` both would be equal to - cos x. Hence x=`pi- pi/3 , pi +pi/3`

or, `(2pi)/3, (4pi)/3`.