Lutasin ang y=cot^-1(frac{sqrt{1+sinx}+sqrt{1-sinx}}{sqrt{1+sinx}-sqrt{1-sinx}})

$$y = \cot ^ { - 1 } ( \frac { \sqrt { 1 + \sin x } + \sqrt { 1 - \sin x } } { \sqrt { 1 + \sin x } - \sqrt { 1 - \sin x } } )$$

I-solve ang y (complex solution)

$$y=\arctan(\frac{-\sqrt{2\left(\cos(2x)+1\right)}+2}{2\sin(x)})$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}$$

I-solve ang x

$$x=arcSin(2SinI(y)CosI(y))+2\pi n_{201}\text{, }n_{201}\in \mathrm{Z}\text{, }\exists n_{32}\in \mathrm{Z}\text{ : }\left(n_{32}<\left(arcSin(2SinI(y)CosI(y))+2\pi n_{201}\right)\pi ^{-1}\text{ and }n_{32}>\left(arcSin(2SinI(y)CosI(y))+2\pi n_{201}+\left(-1\right)\pi \right)\pi ^{-1}\right)\text{ and }\nexists n_{3}\in \mathrm{Z}\text{ : }arcSin(2SinI(y)CosI(y))+2\pi n_{201}=\pi n_{3}$$

$$x=\pi +2\pi n_{202}+\left(-1\right)arcSin(2SinI(y)CosI(y))\text{, }n_{202}\in \mathrm{Z}\text{, }\exists n_{32}\in \mathrm{Z}\text{ : }\left(n_{32}<\left(\pi +2\pi n_{202}+\left(-1\right)arcSin(2SinI(y)CosI(y))\right)\pi ^{-1}\text{ and }n_{202}<\left(-\frac{1}{2}\right)\pi ^{-1}\left(\left(-1\right)arcSin(2SinI(y)CosI(y))+\left(-1\right)\pi n_{32}\right)\right)\text{ and }\nexists n_{3}\in \mathrm{Z}\text{ : }\pi +2\pi n_{202}+\left(-1\right)arcSin(2SinI(y)CosI(y))=\pi n_{3}$$

I-solve ang y

$$y=\arctan(\frac{-\sqrt{-\left(\sin(x)\right)^{2}+1}+1}{\sin(x)})$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}$$