The Wronskian & Variation of Parameters · Medium problem

For $y''+y=\sec t$, the fundamental set $\{\cos t,\sin t\}$ gives $u_1'=-\tan t$. Using the equally valid fundamental set $\{-\cos t,\sin t\}$ instead (with its own Wronskian), find $u_1'$ as a function of $t$ for THIS set.