Q-derivative of q-Sine

Theorem

The following formula holds: $$D_q \mathrm{Sin}_q(bz) = b \mathrm{Cos}_q(bz),$$ where $D_q$ is the q-derivative, $\mathrm{Sin}_q$ is the $q$-Sine function, and $\mathrm{Cos}_q$ is the $q$-cosine function.

References

• 2012: Thomas Ernst: A Comprehensive Treatment of q-Calculus ... (previous) ... (next): (6.170)