2 cosx + tan x - =0

Question

Answer in radians using exact values

Answer 1

2cos(x)+tan(x)-1=0?

2cos(x)+sin(x)/cos(x)-1=0,

2cos²(x)+sin(x)-1=0,

2-2sin²(x)+sin(x)-1=0,

2sin²(x)-sin(x)-1=0=(2sin(x)+1)(sin(x)-1).

So sin(x)=-½ or 1⇒x=2πn-π/6, 2πn+7π/6 or (2n+1)π/2.where n is an integer.