Asked by don
                Solve  cosxtanx + sqroot3cosx - sqroot3/2tanx - 3/2 = 0        
interval 0 to 2 pi
exact answers and formula for the general solution as well as the specific solutions.
Sorry Steve, missed it last night.
            
        interval 0 to 2 pi
exact answers and formula for the general solution as well as the specific solutions.
Sorry Steve, missed it last night.
Answers
                    Answered by
            Steve
            
    If I'm reading it right, we have 
cos tan + √3 cos - √3/2 tan - 3/2 = 0
rearrange terms a bit to get
tan(cos - √3/2) + √3(cos - √3/2) = 0
(tan + √3)(cos - √3/2) = 0
tan x = -√3 --> x = 2pi/3 or 4pi/3
x = (2k+1)*pi +/- pi/3
cos x = √3/2 --> x = pi/6 or 11pi/6
x = k*2pi +/- pi/6
    
cos tan + √3 cos - √3/2 tan - 3/2 = 0
rearrange terms a bit to get
tan(cos - √3/2) + √3(cos - √3/2) = 0
(tan + √3)(cos - √3/2) = 0
tan x = -√3 --> x = 2pi/3 or 4pi/3
x = (2k+1)*pi +/- pi/3
cos x = √3/2 --> x = pi/6 or 11pi/6
x = k*2pi +/- pi/6
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