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From Förberedande kurs i matematik 1

If we use the Pythagorean identity and write sin2x as 1−cos2x, the whole equation written in terms of cosx becomes

21−cos2x−3cosx=0 

or, in rearranged form,

2cos2x+3cosx−2=0

With the equation expressed entirely in terms of cosx, we can introduce a new unknown variable t=cosx and solve the equation with respect to t. Expressed in terms of t, the equation is

2t2+3t−2=0

and this second-degree equation has the solutions t=21 and t=−2 .

In terms of x, this means that either cosx=21 or cos x=−2. The first case occurs when

\displaystyle x=\pm \frac{\pi }{3}+2n\pi ( \displaystyle n an arbitrary integer),

whilst the equation \displaystyle \text{cos }x=-\text{2 } has no solutions at all (the values of cosine lie between \displaystyle -\text{1 } and \displaystyle \text{1} ).

The answer is that the equation has the solutions

\displaystyle x=\pm \frac{\pi }{3}+2n\pi ( \displaystyle n an arbitrary integer).