  Balancing numbers $n$ are originally defined as the solution of the
Diophantine equation $1+2+\cdots+(n-1)=(n+1)+\cdots+(n+r)$, where $r$ is called
the balancer corresponding to the balancing number $n$. By slightly modifying,
$n$ is the cobalancing number with the cobalancer $r$ if
$1+2+\cdots+n=(n+1)+\cdots+(n+r)$. Let $B_n$ denote the $n^{th}$ balancing
number and $b_n$ denote the $n^{th}$ cobalancing number. Then $8B_n^2+1$ and
$8b_n^2+8b_n+1$ are perfect squares. The $n^{th}$ Lucas-balancing number $C_n$
and the $n^{th}$ Lucas-cobalancing number $c_n$ are the positive roots of
$8B_n^2+1$ and $8b_n^2+8b_n+1$, respectively. In this paper, we establish some
trigonometric-type identities and some arithmetic properties concerning the
parity of balancing, cobalancing, Lucas-balancing and Lucas-cobalancing
numbers.
