Question

If y = e^m sin^–1 x and (1 – x²) = Ay², then A is equal to ______.

Options

• m

• – m

• m²

• – m²

Answer 1

If y = e^m sin^–1 x and (1 – x²) = Ay², then A is equal to m².

Explanation:

Given, y = `e^(msin^-1x)`  ...(i)

After differentiating on both sides w.r.t. x, we get

`dy/dx = e^(msin^-1x) d/dx(m sin^-1 x)`

`\implies dy/dx = e^(m^(sin^-1x))(m xx 1/sqrt(1 - x^2))`

`\implies sqrt(1 - x^2) dy/dx` = my  ...[From equation (i)]

After squaring on both sides, we get

`(1 - x^2)(dy/dx)^2` = m²y²

As, `(1 - x^2)(dy/dx)^2` = Ay²

Hence, A = m²