Let f(x)={sin (tan^(−1) x)+sin (cot^(−1) x)}^2 −1 where ∣x∣>1 and (dy/dx)=(1/2)(d/dx)(sin^(−1) f(x)). if y((√3))=(Π/6) then y(−(√3))=?


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Question Number 145814 by gsk2684 last updated on 08/Jul/21
$Let f(x)={sin (tan^(−1) x)+sin (cot^(−1) x)}^2 −1 where ∣x∣>1 and (dy/dx)=(1/2)(d/dx)(sin^(−1) f(x)). if y((√3))=(Π/6) then y(−(√3))=?$
$L e t f (x) = {\sin (\tan^{- 1} x) + \sin (\cot^{- 1} x)}^{2} - 1$ $w h e r e ∣ x ∣> 1 a n d \frac{d y}{d x} = \frac{1}{2} \frac{d}{d x} (\sin^{- 1} f (x)) .$ $i f y (\sqrt{3}) = \frac{Π}{6} t h e n y (- \sqrt{3}) = ?$
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