Hey there!
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It's important to note that the question is a hence question. This implies you have to use the previous parts at some point or other. While this is usually as early as possible in the question, it very occasionally isn't - but luckily, here it definitely is. Thus, we sub in what we just proved in part (ii) to conclude that
From here, it's important to recognise that \(\int \sec ^2x \ dx\) is a standard integral that appears on your reference sheet - and that \(\int \sec x \tan x \ dx\) is given to you as part of the question. Hence, we find that
Hope this helps