Question

Solve the equation on the
interval [0, 2π).
√2 cos x - 1 = 0

Answer 1

Explanation:

`√(2) cos x-1=0\\cos x=(1)/(√(2) ) =cos ((\pi )/(4) ),cos (2\pi -(\pi )/(4) )\\cos x=cos(2n\pi +(\pi )/(4) ),cos(2n\pi +(7\pi )/(4) )\\x=2n\pi +(\pi )/(4) ,2n\pi +(7\pi )/(4) \\n=0\\x=(\pi )/(4) ,(7\pi )/(4)`