Question

If sin y = x cos(a + y), then `dx/dy` is ______.

Options

• `cosa/(cos^2(a + y))`

• `(-cosa)/(cos^2(a + y))`

• `cosa/(sin^2y)`

• `(-cosa)/(sin^2y)`

Answer 1

If sin y = x cos(a + y), then `dx/dy` is `underlinebb(cosa/(cos^2(a + y)))`.

Explanation:

Given, sin y = x cos(a + y)

`\implies x = siny/(cos(a + y))`

Differentiating with respect to y, we get

`dx/dy = (cos(a + y)d/dy (siny) - siny d/dy {cos(a + y)})/(cos^2(a + y))`

`\implies dx/dy = (cos(a + y)cosy - siny[-sin(a + y)])/(cos^2(a + y))`

`\implies dx/dy = (cos(a + y)cosy + sinysin(a + y))/(cos^2(a + y))`

`\implies dx/dy = (cos[(a + y) - y])/(cos^2(a + y))`

`\implies dx/dy = cosa/(cos^2(a + y))`