Question

If sin y = x sin (a + y), then value of dy/dx is

Options

• `(sin(a + y))/sin a`

• `(sin^2(a + y))/sin a`

• `sin^2 (a + y)`

• `(cos^2(a + y))/sin a`

Answer 1

`(sin^2(a + y))/sin a`

Explanation:

sin y = x sin (a + y)

∴ x = `sin y/(sin(a + y))`

Differentiating the function with respect to y

`(dx)/(dy) = (sin(a + y) cos y - sin y cos(a + y))/(sin^2 (a + y))`

= `(sin (a + y - y))/(sin^2 (a + y))`

= `sin a/(sin^2 (a + y))`

∴ `(dy)/(dx) = (sin^2 (a + y))/sin a`