Solve the equation on the interval 0 less than or equals theta less than 2 pi 0≤θ<2π. 2cos^(2)\theta +\sqrt(2cos\theta )=2cos\theta +\sqrt(2)

Answer 1

why do you write "the interval 0 less than or equals theta less than 2 pi" and then go right ahead and say "0≤θ<2π" ? Just like to repeat yourself?

2cos^2θ + √(2cosθ) = 2cosθ + √2

Just by inspection, θ=0
and θ cannot be in QII or QIII, since there cosθ < 0
and since the function is even, solutions in QIV mirror those in QI.