Question

Find all solutions in the interval [0, 2pi] cos^2x+ 2cosx + 1

Answer 1

Let \(u=\cos x\) so we may substitute to yield \(u^2+2u+1=0\). Factor the left-hand side to yield \((u+1)^2=0\), which means \(u=-1\implies\cos x=-1\). Now can you solve?

Answer 2

How do I answer it in the interval [0, 2pi]?