Asked by Karen
Solve the equation for exact solutions in the interval 0 ≤ x < 2π. (Enter your answers as a comma-separated list.)
cos 2x cos x − sin 2x sin x = 0
cos 2x cos x − sin 2x sin x = 0
Answers
Answered by
Reiny
(cos^2 x - sin^2 x)(cosx) - (2sinxcosx)(sinx) = 0
divide by cosx
cos^2 x - sin^2 x - 2sin^2 x = 0
cos^2 x = 3sin^2 x
sin^2 x/cos^2 x = 1/3
tan^2 x = 1/3
tanx = ± 1/√3
so x could in in any of the 4 quadrants
I know tan 30° = 1/√3
and 30° = π/6 radians
so x = 30° , 150° , 210° , 330°
or
x = π/6 , 5π/6 , 7π/6 , 11π/6
divide by cosx
cos^2 x - sin^2 x - 2sin^2 x = 0
cos^2 x = 3sin^2 x
sin^2 x/cos^2 x = 1/3
tan^2 x = 1/3
tanx = ± 1/√3
so x could in in any of the 4 quadrants
I know tan 30° = 1/√3
and 30° = π/6 radians
so x = 30° , 150° , 210° , 330°
or
x = π/6 , 5π/6 , 7π/6 , 11π/6