Differential Equation y' + y cotx = sinx

Hi guys, this is the differentioan equation I need help to solve

**y' + y cotx = sinx**

**attempt:¨**

**'**

This is the case of using an Integration factor as far as I am concerned.

The form of the equation is

dy/dx (with constant 1) + a(x) * y = b(x)

1. I can see that a(x) is in fact cot x . my integration factor will be e^$cot x dx

as cot x is the same as 1/tanx I put it in the I.F instead

Thus e^$1/tanx * dx -> e^ln tan x = I.F = tanx

2. Then i multiply it

tanx * y' + tanx * y cot x = tanx * sinx

as far as I can see, this is not the product rule?

Can someone help me solve this?