Question-20036

Question Number 20036 by mondodotto@gmail.com last updated on 20/Aug/17

Answered by sma3l2996 last updated on 21/Aug/17

2 {s i n}^{- 1} (x \sqrt{6}) = \frac{π}{2} - {s i n}^{- 1} (4 x) \Leftrightarrow s i n (2 {s i n}^{- 1} (x \sqrt{6})) = s i n (\frac{π}{2} - {s i n}^{- 1} (4 x))

2 s i n ({s i n}^{- 1} (x \sqrt{6})) c o s ({s i n}^{- 1} (x \sqrt{6})) = c o s ({s i n}^{- 1} (4 x))

2 x \sqrt{6} \sqrt{1 - 6 x^{2}} = \sqrt{1 - 16 x^{2}}

24 x^{2} (1 - 6 x^{2}) = 1 - 16 x^{2}

24 x^{2} - 144 x^{4} + 16 x^{2} = 1

144 x^{4} - 40 x^{2} = - 1 \Leftrightarrow 144 x^{4} - 2 \times \frac{5}{3} \times 12 x^{2} + \frac{25}{9} = \frac{25}{9} - 1

{(12 x^{2} - \frac{5}{3})}^{2} = \frac{16}{9} \Leftrightarrow x^{2} = \frac{1}{4} o r x^{2} = \frac{1}{36}

x = \frac{1}{2}; \frac{- 1}{2}; \frac{1}{6}; \frac{- 1}{6}