Statics with Trigonometry!

As shown in the figure, the non-stretch light rope AOAO and BOBO are attached to a node OO, OO is attached to an object PP, BO>AOBO>AO, where point AA and BB are fixed on the same horizontal line. At the beginning, AOAO is vertical and the two ropes are just stretched. The tensions of AOAO and BOBO are denoted as FAF_{A} and FBF_{B} respectively. Now, keeping AA and BB on the same horizontal line, if we slowly move point BB to the left, what can we say about FAF_{A} and FBF_{B} as ABAB increases?

Note: Can you rigorously prove it?

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