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I've tried several functions related to trigonometric transformations, namely
TrigReduce, as well as
FunctionExpand and some others, but none gives me the following result (or similar) which I can verify with
FullSimplify[ A Cos[x] + B Sin[x] == Sqrt[A^2+B^2] Sin[x+ArcTan[B,A]] ]
Of course, this is not a simplification of the LHS, so it's unreasonable to expect
FullSimplify to yield it directly, but maybe I'm missing some more functions, which could directly lead me to expression similar to RHS of the above equality (i.e. containing only one $\sin$ or $\cos$ of shifted $x$ instead of superposition of multiple $\sin$-$\cos$es). Are there any such functions?