Question

Solve the equation:
a.) 2 cos^2x-cos x=1

Answer 1

let's define \[t:= \cos(x)\]
we have the quadratic equation:
\[2t^2-t=1\]
can you find it's solutions?

Answer 2

Would it be cos=1? Which means cos=0 degrees or 360 degrees?

Answer 3

there are two solutions, \[\cos(x)=1\]
and \[\cos(x)=-\frac{1}{2}\]
so x can be either
\[360^\circ{} k\] (for every integer k)
or \[120^\circ{}+ 360^{\circ}k\]
or \[240^\circ{}+ 360^{\circ}k\]