Question

Solve cos^2x + 2cosx + 1 = 0 for x over the interval [0, 2pi ). Can someone please give me a step by step answer. I don't understand at all.

Answer 1

Cos²x+2cos x+1=0

We have to do a change of variable.

cos x=t

Then, we have the next square equation.

t²+2t+1=0


We solve this square equation:

t=[-2⁺₋√(4-4)]/2=-1
 if cos x=t  then we have that:

cos x=-1
x=cos⁻¹ -1= π radians    or    180º.

Answer: x=π  (in radians)  or    x=180º   (in degrees).