Question

Find all solutions to the equation.

cos2x + 2 cos x + 1 = 0

Answer 1

rewrite \(\cos(2x)=2\cos^2(x)-1\) and solve that one

Answer 2

in other words, solve
\[2\cos^2(x)-1+\cos(x)+1=0\]

Answer 3

can you explain how to solve it?

Answer 4

first step would be to note that \(1-1=0\) and solve
\[2\cos^2(x)+\cos(x)=0\] then factor as \(\cos(x)\left(2\cos(x)+1\right)=0\)
finally solve
\[\cos(x)=0\] and also \[2\cos(x)+1=0\]
\[2\cos(x)=-1\]
\[\cos(x)=-\frac{1}{2}\]

Answer 5

thank you so much! :)