For part B, how did they cancel out the cot?
You could say its a unique question and method.
If you see trig(something 1) = trig(something 2) you can just cancel out the trig (as long as they are the same) and equate something 1 to something 2.
E.g. sin(x + 50) = sin(100)
x + 50 = 100
x = 50