(i) If a differential equation is ,

then y(I.F) = ∫Q.(I.F)dx + c, where I.F = e^∫Pdx

(ii) ∫tanxdx = log|secx| + c

Given:-

This is a linear differential equation, comparing it with

P = – tanx, Q = – 2 sinx

I.F = e^∫Pdx

= e^∫–tanxdx

= e^–log|secx|

Solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c

⇒ ycosx = –2sinxcosxdx + c₁

⇒ ycosx = –sin2xdx + c₁