We have to solve for x given sin2x-(cos 2x)/2 -1/2=cosx-2cosx*tanx
sin 2x - (cos 2x)/2 -1/2 = cos x - 2cos x * tan x
=> 2 sin x cos x - (1 - 2 (sin x)^2)/2 - 1/2 = cos x - 2cos x * sin x/ cos x
=> 2 sin x cos x - 1 + (sin x)^2 = cos x - 2 sin x
=> 2 sin x cos x - (cos x)^2 = cos x - 2 sin x
=> cos x ( 2 sin x - cos x) = cos x - 2 sin x
=> - cos x = 1
=> cos x = -1
=> x = arc cos -1
=> x = pi
also 2 sin x - cos x = 0
=> 2 sin x = cos x
=> 2 tan x = 1
=> x = arc tan 1/2
Therefore x = arc tan (1/2) and x = pi
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