Rezolvați y=ln(tan^2x)

$$y = \ln ( \tan ^ { 2 } x )$$

Rezolvați pentru y (complex solution)

$$y=\ln(-\frac{\cos(2x)-1}{2\left(\cos(x)\right)^{2}})$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}$$

Rezolvați pentru x

$$x=\pi +\left(-1\right)ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2n_{43}\pi \text{, }n_{43}\in \mathrm{Z}\text{, }\exists n_{6}\in \mathrm{Z}\text{ : }\left(\pi +\left(-1\right)ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2n_{43}\pi >\frac{1}{2}\pi n_{6}\text{ and }\pi +\left(-1\right)ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2n_{43}\pi <\frac{1}{2}\pi \left(n_{6}+1\right)\right)\text{ and }\exists n_{6}\in \mathrm{Z}\text{ : }\left(\pi +\left(-1\right)ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2n_{43}\pi >\frac{1}{2}\pi n_{6}\text{ and }\pi +\left(-1\right)ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2n_{43}\pi <\frac{1}{2}\pi \left(n_{6}+1\right)\right)$$

$$x=2n_{36}\pi +\left(-1\right)\pi +ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})\text{, }n_{36}\in \mathrm{Z}\text{, }\exists n_{6}\in \mathrm{Z}\text{ : }\left(2n_{36}\pi +\left(-1\right)\pi +ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})>\frac{1}{2}\pi n_{6}\text{ and }2n_{36}\pi +\left(-1\right)\pi +ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})<\frac{1}{2}\pi \left(n_{6}+1\right)\right)\text{ and }\exists n_{6}\in \mathrm{Z}\text{ : }\left(2n_{36}\pi +\left(-1\right)\pi +ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})>\frac{1}{2}\pi n_{6}\text{ and }2n_{36}\pi +\left(-1\right)\pi +ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})<\frac{1}{2}\pi \left(n_{6}+1\right)\right)$$

$$x=ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2\pi n_{37}\text{, }n_{37}\in \mathrm{Z}\text{, }\exists n_{6}\in \mathrm{Z}\text{ : }\left(ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2\pi n_{37}>\frac{1}{2}\pi n_{6}\text{ and }ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2\pi n_{37}<\frac{1}{2}\pi \left(n_{6}+1\right)\right)\text{ and }\exists n_{6}\in \mathrm{Z}\text{ : }\left(ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2\pi n_{37}>\frac{1}{2}\pi n_{6}\text{ and }ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})+2\pi n_{37}<\frac{1}{2}\pi \left(n_{6}+1\right)\right)$$

$$x=\left(-1\right)\left(\left(-2\right)\pi n_{38}+ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})\right)\text{, }n_{38}\in \mathrm{Z}\text{, }\exists n_{6}\in \mathrm{Z}\text{ : }\left(\left(-1\right)\left(\left(-2\right)\pi n_{38}+ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})\right)>\frac{1}{2}\pi n_{6}\text{ and }\left(-1\right)\left(\left(-2\right)\pi n_{38}+ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})\right)<\frac{1}{2}\pi \left(n_{6}+1\right)\right)\text{ and }\exists n_{6}\in \mathrm{Z}\text{ : }\left(\left(-1\right)\left(\left(-2\right)\pi n_{38}+ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})\right)>\frac{1}{2}\pi n_{6}\text{ and }\left(-1\right)\left(\left(-2\right)\pi n_{38}+ArcCosI(\left(e^{y}+1\right)^{-\frac{1}{2}})\right)<\frac{1}{2}\pi \left(n_{6}+1\right)\right)$$

Rezolvați pentru y

$$y=\ln(\left(\tan(x)\right)^{2})$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(x>\frac{\pi n_{1}}{2}\text{ and }x<\frac{\pi n_{1}}{2}+\frac{\pi }{2}\right)$$