maths a level trigonometric identities question

I've been staring at this question and I have no idea how to start
Any help would be appreciated!

(identity) transform sin() and cos() to a single (harmonic) trig function as youve been doing on other questions, then simply state the maximum value and the time at which it occurs. No calculus is necessary.

Yep I managed to work out the range of the function by using the transformations and comparing the function with the graph of cosx! At first I was confused because I didn't know how to differentiate trig functions, but I realised you don't need calculus haha

Whenever you have two trig functions like this with the same argument, almost the default is to put them in harmonic form. So sounds like you're good.

You can use calculus and its not that much more work, but its a bit like finding the min/max of a quadratic by completiing the square rather than differentiation. Its easy to "simply read" the turning point values from the expression.