If-sin-1-1-x-2-sin-1-x-pi-2-then-x-

Question Number 90629 by Josephbaraka@gmail.com last updated on 25/Apr/20

If \sin^{- 1} (1 - x) - 2 \sin^{- 1} x = \frac{π}{2}, then x =

Commented by jagoll last updated on 25/Apr/20

l e t \sin^{- 1} (1 - x) = y

1 - x = \sin y \Rightarrow x = 1 - \sin y

{2 \sin}^{- 1} (x) = p \Rightarrow x = \sin (\frac{p}{2})

\Rightarrow \cos (y - p) = 0

\cos y \cos p + \sin y \sin p = 0

\sqrt{2 x - x^{2}} (1 - 2 x^{2}) = (x - 1) (2 x \sqrt{1 - x^{2}})

Answered by TANMAY PANACEA. last updated on 25/Apr/20

{s i n}^{- 1} (1 - x) = \frac{π}{2} + 2 {s i n}^{- 1} x

s i n ({s i n}^{- 1} (1 - x)) = s i n (\frac{π}{2} + 2 {s i n}^{- 1} x)

1 - x = c o s (2 {s i n}^{- 1} x)

s i n θ = x s o c o s 2 θ = 2 {s i n}^{2} θ - 1 = 2 x^{2} - 1

1 - x = 2 x^{2} - 1

2 x^{2} + x - 2 = 0

x = \frac{- 1 \pm \sqrt{1 + 16}}{4} = \frac{- 1 \pm \sqrt{17}}{4}