If y = sin (m sin−1 x), then (1 − x2) y2 − xy1 is equal to

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KollegeApply · Accepted Answer

(c)−m2y Here, y = \sin\left( m \sin^{- 1} x \right) \Rightarrow y_1 = \cos\left( m \sin^{- 1} x \right)m/$\sqrt$(1 - x^2) \Rightarrow y_2 = - \sin\left( m \sin^{- 1} x \right)\frac{m^2}{\left( 1 - x^2 \right)} + \frac{mx\cos\left( m \sin^{- 1} x \right)}{\left( 1 - x^2 \right)^{$\frac{3}{2}$}} \Rightarrow y_2 = - \sin\left( m \sin^{- 1} x \right)\frac{m^2}{\left( 1 - x^2 \right)} + \frac{xm\cos\left( m \sin^{- 1} x \right)}{\left( 1 - x^2 \right) $\times$ $\sqrt$(1 - x^2)} \Rightarrow y_2 = - \sin\left( m \sin^{- 1} x \right)\frac{m^2}{\left( 1 - x^2 \right)} + \frac{x y_1}{\left( 1 - x^2 \right)} \Rightarrow \left( 1 - x^2 \right) y_2 = - y m^2 + x y_1 \Rightarrow \left( 1 - x^2 \right) y_2 - x y_1 = - m^2 y

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