Quick General Solution Trig Question (1 Viewer)

[pikachu975]

Find the general solution of cosx - sqrt(3) sinx = 1
The answer says x = 2n(pi) +- pi/3 - pi/3 but I don't get why. Thanks in advance

 

[Green Yoda]

using auxiliary method
2cos(x+π/3)=1
x+π/3=π/3
x+π/3=2Nπ+-π/3
x=2Nπ+-π/3-π/3
where N is a integer

 

[pikachu975]

Thanks, I accidentally did x + pi/3 = pi/3, 5pi/3...
But I minused the pi/3 first so I got it wrong, thanks for the help.

 

[Orthos]

√3 sin(x) = cos(x) - 1
3sin^2(x) = cos^2(x) - 2cos(x) + 1
2cos^2(x) - cos(x) - 1 = 0
(2cos(x) + 1)(cos(x) - 1) = 0