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

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Answer 1 · 2016-12-12T19:19:55

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

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, $(2pi)/3, (4pi)/3$ .

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