Question

Choose the correct option from the given alternatives :

If y = sin (2sin^–1 x), then _dx = ........

Options

• `(2 - 4x^2)/sqrt(1 - x^2)`

• `(2 + 4x^2)/sqrt(1 - x^2)`

• `(4x^2 - 1)/sqrt(1 - x^2)`

• `(1 - 2x^2)/sqrt(1 - x^2)`

Answer 1

`(2 - 4x^2)/sqrt(1 - x^2)`

[Hint : y = sin(2sin^–1 x)
Put x = sinθ. Thenθ = sin^–1x
∴ y = sin2θ

∴ `"dy"/"dx" = "dy"/"dθ" xx "dθ"/"dx" = 2cos2θ xx (1)/sqrt(1 - x^2)`

= `(2(1 - 2sin^2θ))/sqrt(1 - x^2)  = (2 - 4x^2)/sqrt(1 - x^2)`].