Question

sin inverce(dy/dx) =X+y​

Answer 1

Hope this answer help you and also it make me brainlist

Answer 2

Answer:

sin⁻¹(dy/dx) = x + y

==> (dy/dx) = sin(x + y)    ---- (i)

Let x + y = u.

Differentiate with respect to x.

==> 1 + dy/dx = du/dx

==> dy/dx = du/dx - 1

Place the value of dy/dx in (i)

==> (du/dx) - 1 = sin u

==> (du/dx) = 1 + sinu

==> ∫(du/1+sinx) = ∫dx

==> ∫(1 - sinu/1 - sin²u) du = x + c

==> ∫(1 - sinu/cos²u) du = x + c

==> ∫(sec²u - secutanu) du = x + c

==> ∫sec²u - ∫tanusecu du = x + c

==> tanu - secu = x + c

• tan(x + y) - sec(x + y) = x + c