Could I get some guidance on this subject?

Yfrog - vh5.jpg Yfrog - dsc04451z
I thought I could do the first one by starting from the right. I figured I could replace du/ds with du/dx (dx/dt), replace dx/dt with the derivative given by the info, get e^2s and sin^2 + cos ^2 as a multiplier and end up with the left side. However, du/ds leaves cost as cost and only du/dt gives me a cos^2 so I don't get that clean 1. Am I missing something, made a great mistake, or just approaching this entirely wrongly?