Solve the equation (2/arctanx)-arctanx=1

Expert Answers

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We have the equation 2/arc tanx - arc tanx = 1 to solve.

let y = arc tan x.

2/arc tanx - arc tanx = 1

=> 2/y - y = 1

mutiply all the terms with y

=> 2 - y^2 = y

move the terms to one side

=> y^2 + y - 2  = 0

y1 = [-b + sqrt ( b^2 - 4ac] / 2a

= [ -1 + sqrt (1 + 8)] / 2

= [ -1 + sqrt 9]/2

=> 1

y2 = -1/2 - 3 / 2

y2 = -2

As y = arc tan x

arc tan x = 1

=> x = tan 1

arc tan x = -2

=> x = - tan 2

Therefore x is equal to tan 1 and -tan 2.

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