A ball of mass m, moving with speed u, hits another resting ball of the same mass. After the collision

A ball of mass m, moving with speed u, hits another resting ball of the same mass. After the collision, the first ball changed its direction of motion by an angle α. Find the velocity of the balls after impact if the impact is absolutely elastic.

In an elastic off-center collision, the balls fly off at an angle of 90. This can be used to solve the problem. Let us write a system in which there are two equations: the law of conservation of the projection of momentum on the x and y axes.
We get:
m * u = m * v1 * cos a + m * v2 * cos (90 – a);
m * v1 * sin a = m * v2 * sin (90-a);
Find u:
u = v1 * cos a + v2 * sin a;
v1 * tg a = v2;
u = v1 * (cos a + tg a * sin a);
v1 = u / (cos a + tg a * sin a);
v2 = u * tg a / (cos a + tan a * sin a).