circle part 2 doubts

Solve the eqn cot alpha + cot beta to get a relation between alpha and beta. ...(I)
The distance between O centre and P(x,y) is(x²+y²)^1/2.

Find the value of sin alpha or beta in terms of radius and the distance OP.... (II)
Now, use the (I) and (II) to get the eqn of locus of point P.

Hint: You can also use beta as the external angle to the triangle containing beta nad the point P to your advantage. The line joining O and P is bisecting the minor angle P.
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