cos-1-2x-2-1-2x-2-cos-1-x-2-2-x-2-120-2pi-3-Find-x-

Question Number 61511 by Kunal12588 last updated on 03/Jun/19

{c o s}^{- 1} \frac{2 x^{2} - 1}{2 x^{2}} + {c o s}^{- 1} \frac{x^{2} - 2}{x^{2}} = 120 ° = \frac{2 π}{3}

Find x

Answered by MJS last updated on 03/Jun/19

\cos^{- 1} \frac{2 x^{2} - 1}{2 x^{2}} + \cos^{- 1} \frac{x^{2} - 2}{x^{2}} = \frac{2 π}{3}

π - \sin^{- 1} \frac{2 x^{2} - 1}{x^{2}} - \sin^{- 1} \frac{x^{2} - 2}{x^{2}} = \frac{2 π}{3}

\sin^{- 1} \frac{2 x^{2} - 1}{x^{2}} = \frac{π}{3} - \sin^{- 1} \frac{x^{2} - 2}{x^{2}}

\frac{2 x^{2} - 1}{2 x^{2}} = - \frac{x^{2} - 2 - \sqrt{3 (x^{2} - 1)}}{2 x^{2}} [beware of false solutions!!!]

\Rightarrow x = \pm 1 [false!] \lor x = \pm \frac{\sqrt{21}}{3}

Commented by Kunal12588 last updated on 04/Jun/19

t h a n k y o u s i r

Commented by Kunal12588 last updated on 04/Jun/19

h o w d i d y o u k n o w x = \pm 1 i s f a l s e

Commented by Kunal12588 last updated on 04/Jun/19

\frac{2 x^{2} - 1}{2 x^{2}} = - \frac{x^{2} - 2 - 2 \sqrt{3 (x^{2} - 1)}}{2 x^{2}} s i r