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Question Number 19385 by NEC last updated on 10/Aug/17

$${tan}^2\beta =-1$$$$$$$$find\beta ....letssolveforfun$$

Commented by NEC last updated on 10/Aug/17

$$pleasehelp$$

Commented by Tinkutara last updated on 10/Aug/17

$$\mathrm{There}\mathrm{is}\mathrm{no}\mathrm{such}\beta \left(\mathrm{real}\mathrm{or}\mathrm{complex}\right).$$

Commented by NEC last updated on 10/Aug/17

$$the\beta couldalsoberepresentedby$$$$x\mathit{o}\mathit{r}\theta \mathit{o}\mathit{r}\mathit{a}\mathit{n}\mathit{y}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}.$$$$$$$$\mathit{A}friendactuallygavemethe$$$$question{i}^{\prime }mstocked.$$$$$$$$thiswaswhatidid$$$${\mathit{t}\mathit{a}\mathit{n}}^2\mathit{x}=-1$$$${\mathit{t}\mathit{a}\mathit{n}}^2\mathit{x}+1=0$$$${\mathbf{sec}}^2\mathbf{x}=0$$$$\frac{1}{{\mathbf{cos}}^2\mathbf{x}}=0$$$$$$$$$$$$\mathbf{from}\mathbf{that}\mathbf{point}\mathbf{i}\mathbf{became}$$$$\mathbf{confused}.....$$$$\mathbf{i}\mathbf{know}\mathbf{it}\mathbf{might}\mathbf{lead}\mathbf{to}\mathbf{a}\mathbf{complex}$$$$\mathbf{number}\mathbf{but}\mathbf{if}\mathbf{its}\mathbf{possible}{\mathbf{i}}^{\prime }lllike$$$$toseethesolution$$

Commented by Tinkutara last updated on 10/Aug/17

$$\mathrm{It}\mathrm{is}\mathrm{impossible}.\mathrm{Let}z=e^{i\theta }=\cos \theta +$$$$i\sin \theta \mathrm{and}\overline{z}=e^{-i\theta }=\cos \theta -i\sin \theta .$$$$z+\overline{z}=2\cos \theta =e^{i\theta }+e^{-i\theta }$$$$\frac{1}{\cos \theta }=\frac{2}{e^{i\theta }+e^{-i\theta }}=\frac{2e^{i\theta }}{e^{2i\theta }+1}\mathrm{and}\mathrm{this}$$$$\mathrm{equal}\mathrm{to}0\mathrm{implies}\mathrm{that}{e}^{i\theta }=0\mathrm{which}\mathrm{is}$$$$\mathrm{impossible}.$$

Commented by NEC last updated on 10/Aug/17

$$thanks$$

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