The Wronskian & Variation of Parameters · Medium problem

Using variation of parameters with $y_1=\cos t,\ y_2=\sin t$, the equation $y''+y=\sec t$ (on $-\tfrac\pi2<t<\tfrac\pi2$) has particular solution $y_p(t)=t\sin t+\cos t\ln|\cos t|$. Find $\displaystyle\lim_{t\to(\pi/2)^-}\dfrac{y_p(t)}{t}$.