express this complex trig equation 2cosx+2=secx

Question

express in comples trig equation

Answer 1

2cos(x)+2=sec(x),

2cos²(x)+2cos(x)=1,

cos²(x)+cos(x)=½,

cos²(x)+cos(x)+¼=¾,

(cos(x)+½)²=¾,

cos(x)+½=±√3/2,

cos(x)=-½±√3/2; x=1.1961radians approx. (cosine must lie between -1 and 1, so other "solution" is rejected.)

x=-1.1961radians, so the more general answer is 2πn±1.1961 radians, where n is an integer.

This can also be written 360n°±68.5293°.