A particle attached to two rods, moving in a horizontal circle, will produce forces in the rods which balance vertically and produce a force directed towards the centre of the circle which keep the partilce moving in the circle. We can find the forces in the rods by resolving vertically and horizontally.
Resolving vertically for the particle gives
(1)
Applying
horizontally gives
(2)
(2) gives
but
so the last equation becomes
Hence
Similarly, 
gives
Now use
and divide by
to give
