4(a)

The equation is linear. An integrating factor is

$$\mu(x) = \exp\left( -\int \tan x\, dx\right) = \exp(\ln \cos x) = \cos x$$

The general solution is

$$y = \frac{1}{\cos x} \left(\int -2 \cos x \sin x\, dx + C\right) = \cos x + C/\cos x$$

For the initial condition we have C=0, so $y = \cos x$.