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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)`
Solution
`(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)`].
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