Question

The equation of tangent to the curve y = `sin^-1  (2x)/(1 + x^2)` at x = `sqrt(3)` is ______.

पर्याय

• `y = -1/2(x - sqrt(3))`

• `y - π/3 = -1/2(x - sqrt(3))`

• `y + π/3 = -1/2(x - sqrt(3))`

• None of these

Answer 1

The equation of tangent to the curve y = `sin^-1  (2x)/(1 + x^2)` at x = `sqrt(3)` is `underlinebb(y - π/3 = -1/2(x - sqrt(3)))`.

Explanation:

y = `sin^-1  (2x)/(1 + x^2) = π - 2tan^-1x, "for"  x > 1`

or `dy/dx = -2/(1 + x^2)`

or `(dy/dx)_(x = sqrt(3)) = -2/(1 + 3) = -1/2`

Also, when x = `sqrt(3)`, y = `π - 2 xx π/3 = π/3`

Hence, equation of tangent is `y - π/3 = -1/2(x - sqrt(3))`.