How to solve the ecuation Arctan((x-1)/(x-2))+Arctan((x+1)/(x+2))=(Pi/4) ?

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How to solve the ecuation Arctan((x-1)/(x-2))+Arctan((x+1)/(x+2))=(Pi/4) ?

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Answer 1 · 2018-07-05T08:23:27

$arctan (\frac{x - 1}{x - 2}) + arctan (\frac{x + 1}{x + 2}) = \frac{π}{4}$ $Arctan((x-1)/(x-2))+Arctan((x+1)/(x+2))=pi/4$

$\Rightarrow arctan ⎛ ⎝ \frac{\frac{x - 1}{x - 2} + \frac{x + 1}{x + 2}}{1 - \frac{x^{2} - 1}{x^{2} - 4}} ⎞ ⎠ = \frac{π}{4}$ $=>Arctan(((x-1)/(x-2)+(x+1)/(x+2))/(1-(x^2-1)/(x^2-4)))=pi/4$

$\Rightarrow \frac{x^{2} + x - 2 + x^{2} - x - 2}{x^{2} - 4 - x^{2} + 1} = 1$ $=>(x^2+x-2+x^2-x-2)/(x^2-4-x^2+1)=1$

$\Rightarrow 2 x^{2} - 4 = - 3$ $=>2x^2-4=-3$

$\Rightarrow x = \pm \frac{1}{\sqrt{2}}$ $=>x=pm1/sqrt2$

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How to solve the ecuation Arctan((x-1)/(x-2))+Arctan((x+1)/(x+2))=(Pi/4) ?

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