Solve the equation on the interval

Question

Cos^2theta+2cos theta+1=0

Answer 1

cos^2theta+2cos theta+1=0

Let cos theta = x

x^2+2x+1=0

solve the quadratic equation

(x+1)^2=0

x=-1

cos theta =-1

cos theta = cos (pi)

Write the general solution

theta = 2npi+pi =pi(2n+1)